Flashback subplots?

They suck.

But if you're hellbent on doing it, make it SUPER SUPER short.

Just my opinion.

If done well, I think they can be very interesting, but they can be problematic as well. I've had readers get confused by them - likely because they are reading very quickly and not paying attention - so tread carefully. They can also be viewed as gimmicky by many.

I try to stay away from flashbacks like the kiss of death. My Sister's Keeper did what you're talking about, although the flashbacks were more part of the larger plot than a subplot; this is the only book I've read that handle flashbacks well.

Oh, and The Archived handled flashbacks very well also. If you like urban fantasy I highly recommend this book.