If it is web application you can't show PDF content using FLEX. if it is AIR application you can show the PDF content. Please go through the below link
do convertion server-side to format accessible in Flash runtime
open new window (new location) in browser so user can see pdf content in separate window via PDF plugin
depending on content you could be able to extract it all-client side and show in Flash runtime:
use air runtime or 3rd party solutions for non-web browser based solutions (so you would be able to embed pdf in your application directly).