Watch the Travis Picking: Use online guitar lesson by Walter Broes from Rock, Billy, & Boogie Guidebook
Thumbpicking has become a genre in itself, with practitioners around the globe; a club of enthusiasts with the late great Chet Atkins as a spiritual president. In the context of rockabilly, you can take it as far as you want, although a basic grasp of it should be enough to get by.
The earlier recordings of both Merle Travis and Chet Atkins would be a good place to start of course, as it's the music that directly influenced the 50’s rock and roll generation. Ragtime music, as played by Blind Blake or the Reverend Gary Davis, is very interesting in this context too, being similar in a lot of ways but with a bluesier slant.