The actual material is a satin or silk that is almost the same shade of blue/purple as the pattern on the shirt.
The stripes are actually broken (dashed) pinstripes that are a slightly lighter shade of the base color. the best picture I have found is in the Art of The Dark Knight and that wasn't much.
It is certainly a custom print, just like the shirt.
Unable to find the exact material, or anything remotely close, I settled on this for the back of my vest... (details below)
Originally, a Donald Trump brand men's extra large dress shirt that was a pale blue. I wear a men's small, so one shirt was enough to make the back of the vest, the lining, and pocket lining. I am saving the shirt buttons to use on my hexagon shirt...
It is 100% cotton, but has that satin shine to it. The pinstripes are a weave in the material, so it dyes really well.
I used Navy Blue Rit Dye for a very quick 5 minute dip. It combines with the original color of the shirt to make a very close match to the actual material. The closest that I have found. (Photo above uses a flash)
Once again, I hope anything I post about my own costume has helped others in any way...