Is it possible to incorporate Flask with Pyramid?
Yes; they are both WSGI apps. Just configure a router container to hold them, and map URL prefixes to one or the other. How you do this depends on your WSGI server (some have native support).
Alternatively, have Flask host the Pyramid WSGI app; any Flask route that returns an object that is not a string or a Response object, will be treated as a WSGI app and have the correct data passed in.
I'm building a Pyramid application, but I would like to have a light-weight REST API built in to it. I've built such an API already with Flask, so is it possible to build my application in both Flask and Pyramid simultaneously?