I'm making a game w/ the source port ZDoom, It & ID Tech 1 are open source, & I'm using open source textures, UI, & sounds. Would it be legal for me to make my own flavor of ZDoom on the Android store running my game? I'm going to credit all the original devs.

In principle yes, but you have to abide by all of the relevant licenses. For example, ZDoom contains GPL code, so you must make your own source code available under the GPL or a compatible license.