We believe sinners will be annihilated after the Millennium - not immediately after they die. They will be resurrected mind, body, and soul. Each will suffer punishment in duration and in intensity proportionate to their sinfulness and then they will die eternally.

Yes, according to the definition you quoted:

Which of the 28 Fundamental Beliefs of the SDA Church are being used to substantiate this?

Number 27, take a look:

The millennium is the thousand-year reign of Christ with His saints in heaven between the first and second resurrections. During this time the wicked dead will be judged; the earth will be utterly desolate, without living human inhabitants, but occupied by Satan and his angels. At its close, Christ with His saints and the Holy City will descend from heaven to earth. The unrighteous dead will then be resurrected, and with Satan and his angels will surround the city; but fire from God will consume them and cleanse the earth. The universe will thus be freed of sin and sinners forever. (Rev. 20; 1 Cor. 6:2, 3; Jer. 4:23-26; Rev. 21:1-5; Mal. 4:1; Eze. 28:18, 19.)

Now lets take a look at what the Bible says will happen to the Wicked...

Job 21:30 King James Version (KJV)
"30 That the wicked is reserved to the day of destruction? they shall be brought forth to the day of wrath."

Psalm 37:10 King James Version (KJV)
"10 For yet a little while, and the wicked shall not be: yea, thou shalt diligently consider his place, and it shall not be."

Psalm 37:20 King James Version (KJV)
"20 But the wicked shall perish, and the enemies of the Lord shall be as the fat of lambs: they shall consume; into smoke shall they consume away."

Psalm 37:28 King James Version (KJV)
"28 For the Lord loveth judgment, and forsaketh not his saints; they are preserved for ever: but the seed of the wicked shall be cut off."

Psalm 37:38 King James Version (KJV)
"38 But the transgressors shall be destroyed together: the end of the wicked shall be cut off."

Psalm 73:17-18 King James Version (KJV)
"17 Until I went into the sanctuary of God; then understood I their end.18 Surely thou didst set them in slippery places: thou castedst them down into destruction."

Psalm 92:7 King James Version (KJV)
"7 When the wicked spring as the grass, and when all the workers of iniquity do flourish; it is that they shall be destroyed for ever:"

Psalm 104:35 King James Version (KJV)
"35 Let the sinners be consumed out of the earth, and let the wicked be no more. Bless thou the Lord, O my soul. Praise ye the Lord."

Psalm 145:20 King James Version (KJV)
"20 The Lord preserveth all them that love him: but all the wicked will he destroy."

Proverbs 2:22 King James Version (KJV)
"22 But the wicked shall be cut off from the earth, and the transgressors shall be rooted out of it."

Nahum 1:9-10 King James Version (KJV)
"9 What do ye imagine against the Lord? he will make an utter end: affliction shall not rise up the second time.10 For while they be folden together as thorns, and while they are drunken as drunkards, they shall be devoured as stubble fully dry."

Malachi 4:1King James Version (KJV)
"4 For, behold, the day cometh, that shall burn as an oven; and all the proud, yea, and all that do wickedly, shall be stubble: and the day that cometh shall burn them up, saith the Lord of hosts, that it shall leave them neither root nor branch."

2 Thessalonians 1:8-9 King James Version (KJV)
"8 In flaming fire taking vengeance on them that know not God, and that obey not the gospel of our Lord Jesus Christ:9 Who shall be punished with everlasting destruction from the presence of the Lord, and from the glory of his power;"

2 Peter 2:6 King James Version (KJV)
"6 And turning the cities of Sodom and Gomorrha into ashes condemned them with an overthrow, making them an ensample unto those that after should live ungodly;"

2 Peter 2:9-12 King James Version (KJV)
9 The Lord knoweth how to deliver the godly out of temptations, and to reserve the unjust unto the day of judgment to be punished:10 But chiefly them that walk after the flesh in the lust of uncleanness, and despise government. Presumptuous are they, selfwilled, they are not afraid to speak evil of dignities.11 Whereas angels, which are greater in power and might, bring not railing accusation against them before the Lord.12 But these, as natural brute beasts, made to be taken and destroyed, speak evil of the things that they understand not; and shall utterly perish in their own corruption;

2 Peter 3:7 King James Version (KJV)
"7 But the heavens and the earth, which are now, by the same word are kept in store, reserved unto fire against the day of judgment and perdition of ungodly men."

2 Peter 3:9-10 King James Version (KJV)
"9 The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance.10 But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up. "

Revelation 20:9 King James Version (KJV)
"9 And they went up on the breadth of the earth, and compassed the camp of the saints about, and the beloved city: and fire came down from God out of heaven, and devoured them."

Revelation 21:8 King James Version (KJV)
"8 But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death."

And the words of Christ...

Matthew 7:13 King James Version (KJV)
"13 Enter ye in at the strait gate: for wide is the gate, and broad is the way, that leadeth to destruction, and many there be which go in thereat:"

Matthew 10:28 King James Version (KJV)
"28 And fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell."

Matthew 13:40-42 King James Version (KJV)
"40 As therefore the tares are gathered and burned in the fire; so shall it be in the end of this world.41 The Son of man shall send forth his angels, and they shall gather out of his kingdom all things that offend, and them which do iniquity;
42 And shall cast them into a furnace of fire: there shall be wailing and gnashing of teeth."

Matthew 25:41 King James Version (KJV)
"41 Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:"

Luke 13:3 King James Version (KJV)
"3 I tell you, Nay: but, except ye repent, ye shall all likewise perish."

John 3:14-16 King James Version (KJV)
"14 And as Moses lifted up the serpent in the wilderness, even so must the Son of man be lifted up:15 That whosoever believeth in him should not perish, but have eternal life.16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.

why would anyone believe the wicked are going to burn forever and ever? it says so in the Revelation, but it also says that death and hades are going to be cast in the lake of fire. how does one pick up death and the grave with the hand to throw them away?

this debate lends itself to a deeper discussion about literary interpretation, something that lay people are not qualified to address; hence martin luther's backtrack about the bible in the hand of the common man. he strongly advocated for it at first, but seeing the strange and weird being espoused as TRUTH caused him to seriously rethink the idea

perhaps sda need to revisit the doctrines its theologically unqualified founders sought to lay down as denominational pillars every five years or so in light of recent scholarship lest they end up like the jews: murdering the innocent, unable to see that the old covenant had given way to the new

I am seeing this idea that the pillars of Adventist beliefs and our doctrines supported by the testimonies and anchored soundly in the scripture, be cast aside, thrown away, discarded and they be "revisited" as they are from "theologically unqualified founders". It is being pushed subtly or even stronger by those who claim they are Adventist or "in the church", and yet want all the solid foundation Adventism is anchored on be swept away and dashed into pieces. Satan is angry that the truth given to us still stands and is using his old tactics to conquer and divide from within. We need to stand firm and more fully grasp what God gave His remnant church and people in these last days as many will come with what is claimed as 'new light' or higher 'scholarship' to sweep it all away. We need to follow what God says, not man and not be taken in or shaken off the path so near to the end.