I am currently failing in my endeavor to go fixed.

I have a Schwinn World Sport from about 86ish. Currently I am trying to put an 1/8 crank on the old square taper bottom bracket. The rear hub is a flip flop hub. Currently the chainline does not line up at all.

Do I need a certain bottom bracket? Thanks for the help.

Yes you need the correct spindle length which will depend on your crankset, the information shouldn't be hard to find.

Thanks I've been looking into that.

I've come to the conclusion that I need a 68 mm x 107(-110) mm bottom bracket. How do I know what the TPI is?

What kind of frame do you have, its most likely english thread.

edit: dur its a world sport,than I am almost positive it is english threaded 1.370" X 24 tpi (I don't know why its underlining, but it wont stop)

Pick up a 107mm Shimano UN-54. You'll be all set.