How you go about this really depends on what you're trying to accomplish. Do you need to be able to show lots of different PDFs, that users can upload and other users can view? Do you care if people can print them out? Do you need the PDFs to be indexed, searchable, etc? Do CMYK PDF files have to work?
There's no way to simply view a PDF in Flash. The solutions shown here either
convert a PDF to an SWF publication, which can then be loaded up and displayed with FlashPaper or lvolume's viewer code; or else they just download the PDF file for the user.
We had to do a custom solution for this once, to make it difficult for someone to download a whole PDF file, but make them readable to certain users online. We used the ps2image kit on the server side to image one page of the PDF at a time. And for documents we wanted to index, we had our creator upload them to the system along with a plaintext version with custom markup showing section headers to index, which we stored in a DB. We use Flash just to display the tools to move through the document, but it only comes in one JPG at a time off the server, and the image is then destroyed. However, this is for a system where employees are only allowed secured on-site access, and the goal was paranoia, to prevent these documents from leaking. Probably overkill for what you need.