I don't know what sect wrongly teaches that flesh enters Heaven.
Flesh and blood cannot inherit the kingdom of God, nor does the perishable inherit the imperishable.
Hello ButterflyJones, no one teaches that our fallen, earthly bodies are what we will have in the eternity to come, rather, the whole of the church teaches that at the resurrection of the dead, we will be given new, glorified/spiritual bodies, bodies that are suited for eternal life in the new age/on the new earth.
1 Corinthians 15
39 All flesh is not the same: Men have one kind of flesh, animals have another, birds another and fish another.
40 There are also ~heavenly bodies~ and there are ~earthly bodies~, but the splendour of the heavenly bodies is one kind, and the splendour of the earthly bodies is another.
41 The sun has one kind of splendour, the moon another and the stars another; and star differs from star in splendour.
42 So will it be with the resurrection of the dead. The ~body~ that is sown is perishable, it is raised imperishable;
43 it is sown in dishonour, it is raised in glory; it is sown in weakness, it is raised in power;
44 it is sown a natural body, it is raised a spiritual body. If there is a natural body, there is also a spiritual body.
45 So it is written: “The first man Adam became a living being”; the last Adam, a life-giving spirit.
46 The spiritual did not come first, but the natural, and after that the spiritual.
47 The first man was of the dust of the earth, the second man from heaven.
48 As was the earthly man, so are those who are of the earth; and as is the man from heaven, so also are those who are of heaven.
49 And just as we have borne the likeness of the earthly man, so we shall bear the likeness of the man from heaven.
The one body is described in terms of its essential characteristics as earthly, on the one hand, and therefore belonging to the life of the present age, and as heavenly, on the other, and therefore belonging to the life of the Spirit in the age to come.
It is “spiritual,” not in the sense of “immaterial”, but of “supernatural”.
The transformed body, therefore, is not composed of “spirit”; it is a body adapted to the eschatological existence that is under the ultimate domination of the Spirit. We will bear the likeness of Christ (v. 49) in a transformed body, fitted for the new age. ~Fee, Gordon, NICNT, Commentary, 1st Epistle to the Corinthians
~Deuteronomy
p.s. - here are three passages to consider if you'd care to, the first one is prior to the Lord's resurrection. Here He talks to His disciples and tells them that the next time that He drinks wine with them will be in His Father's Kingdom.
The final two passages happen after His resurrection. Take note that His now resurrected/glorified body is not an immaterial vapor of some sort, rather, He points out to them that it is made up of "flesh and bones" (now glorified, of course).
Matthew 26
26 While they were eating, Jesus took some bread, and after a blessing, He broke it and gave it to the disciples, and said, “Take, eat; this is My body.”
27 And when He had taken a cup and given thanks, He gave it to them, saying, “Drink from it, all of you;
28 for this is My blood of the covenant, which is poured out for many for forgiveness of sins.
29 “But I say to you, I will not drink of this fruit of the vine from now on ~until that day when I drink it new with you in My Father’s kingdom.~”
Luke 24
36 While they were telling these things, Jesus Himself stood in their midst and said to them, “Peace be to you.”
37 But they were startled and frightened and thought that they were seeing a spirit.
38 And He said to them, “Why are you troubled, and why do doubts arise in your hearts?
39 “See My hands and My feet, that it is I Myself; touch Me and see, for a spirit does not have flesh and bones as you see that I have.”
40 And when He had said this, He showed them His hands and His feet.
41 While they still could not believe it because of their joy and amazement, He said to them, “Have you anything here to eat?”
42 They gave Him a piece of a broiled fish;
43 and He took it and ate it before them.
John 20
24 Thomas, one of the twelve, called Didymus, was not with them when Jesus came.
25 So the other disciples were saying to him, “We have seen the Lord!” But he said to them, “Unless I see in His hands the imprint of the nails, and put my finger into the place of the nails, and put my hand into His side, I will not believe.”
26 After eight days His disciples were again inside, and Thomas with them. Jesus came, the doors having been shut, and stood in their midst and said, “Peace be with you.”
27 Then He said to Thomas, “Reach here with your finger, and see My hands; and reach here your hand and put it into My side; and do not be unbelieving, but believing.”
28 Thomas answered and said to Him, “My Lord and my God!”
29 Jesus said to him, “Because you have seen Me, have you believed? Blessed are they who did not see, and yet believed.”