Seems like the sleeves are fine. It's a well fitting jacket, so I hope you've the matching pants to go with it somewhere. I don't have the same knee jerk reaction to an orphan suit jacket that many do around here--but with the peak lapels, that's really pushing it.
A white linen square would've been a better option. If you want silk, probably anything with a navy as a secondary color provided it doesnt clash.
I don't think it is part of a suit. Here is another picture. The material actually feels like a lightweight tweed. I could be wrong though.