I'm starting to play bluegrass flatpicking tunes, but instead of using a flatpick, I use a thumbpick and fingerpicks.
Lester Flatt played this way, as ldpayton mentioned, but he only played rhythm. Wayne Henderson uses a very similar technique to play bluegrass flatpicking style leads, like in this video.
I'd tried flatpicking for a long time, but could never relax enough to make it work. I've been playing Travis style almost since I started playing, so when I recently started playing with Wayne's technique, the bluegrass started to fall into place.