Well, there are two ways I could think of doing it quickly:
1) Write a Flash reader for PDF files. This is not an attractive solution, but could be done with a lot of time, and a lot of patience. Better yet would be to write a PDF->SWF exporter of some kind, which would still be a pain, but easier in all likelihood.
2) Using pre-existing PDF tools, drum up an application that could run from the Linux underbelly (in other words, bypass the Flash layer altogether and write a straight C/C++/etc application to be a flash reader and dump its output to /dev/fb or whatever device they're using for video output ).
2 would be much faster to implement I would believe, but would leave the "Chumbian" way of thinking. The last option I can think of is if someone gets a web browser up and running on the device, to just read ebooks using a PDF plugin for the browser, but that'd likely put you over the memory available, which is probably the hardest part about the whole thing.
The HTML route would be much easier and less painful to implement, as Flash already has some tools around to deal with it.
So in short, it's definitely possible, it'll just take some thinking on how to implement it best for the Chumby platform.