I'm not sure if you could say this is a Baptist belief in regard to tongues, but after recently researching the topic and having discussions with various peers, I will share what has been revealed to me from the scriptures. Doesn't mean i'm entirely right or anything, just what I've read.
Tongues were first and foremost a sign for unbelievers during the time of the Apostles. 1 Cor. 14:22, "Wherefore tongues are for a sign, not to them that believe, but to them that believe not: but prophesying serveth not for them that believe not, but for them which believe."
One of the explicit requirements for tongues in the church is there has to be someone to interpret the tongues before they should be spoken in the church. 1 Cor. 14:27-28, "If any man speak in an unknown tongue, let it be by two, or at the most by three, and that by course; and let one interpret. But if there be no interpreter, let him keep silence in the church; and let him speak to himself, and to God."
The Apostles had the ability to show signs for non-believers, as tongues was. The Apostles could pass these abilities on to others, but those others couldn't further pass on the abilities. Just as an Apostle could touch a piece of cloth and however touched that cloth would be healed, but that person couldn't do the same with another piece of cloth. In 1 Cor. 13:8 it says, "Charity never faileth: but whether there be prophecies, they shall fail; whether there be tongues, they shall cease; whether there be knowledge, it shall vanish away." These things were spiritual gifts. Knowledge, for instance, doesn't mean knowledge as in learning, but instant knowledge given by the God, not learned. Why did these things cease? We now have the word of God, to study, to give us hope, to give us comfort. The word of God is complete and those things have passed away. 1 Cor. 13:12 says, "For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known."
There are some other angles to the subject, but I don't want to start anything negative, so i'll just stick with these verses
Edit -> I am Baptist, but not Southern Baptist. I'm Primitive Baptist, and from discussions with peers (not only Primitive Baptists) the above is relatively close to most Baptist beliefs.