I bought a trek 311 frame and fork from CL IN hopes of creating my first single speed. It came with 68mm x 118mm bb spindle(for a double). I understand to keep the chain line, I'd need to buy a shorter spindle bracket to pull the single in closer to the frame. How much should I go in? I looked on amazon for the sealed bracket replacements and the shortest they have is a 68mm x 107mm. Would that work ?

Will you be using the stock crank and just removing one ring or buying a new crankset?

The required spindle length always depends on the crankset being used, never the frame.

Depends on what cranks you're planning on using but a good ROT is to measure the space between the two chainrings and halve it, then subtract that number from your spindle length, and that'll be the length you'll want. Of course as Scrod said, that's if you're using the same cranks