I googled for methods to render PDF in AIR with Flash. But most of examples were for Flex applications. Actually it also very simple to render PDF with Flash (pure ActionScript project instead of Flex project).

The most important thing for rendering PDF in Flash, the stage scale mode must be NO_SCALE, while by default, a pure ActionScript AIR application running in SHOW_ALL mode.

PDF in AIR Application, Limitations

Although PDF and Flash both technologies from Adobe, in AIR seems they’re separated, PDF always render on top of AIR stage, not really added into display list inside Flash. PDF can be controlled through Javascript, but nothing else. Very limit functionality.

AIR 2 support to open PDF files with native default application, which might be more friendly for users than put PDF inside an AIR application.