You’re right, AE doesn’t have the Continuously Rasterize Button, available for the swf layer in the timeline window. Hmmm.
Guess you’ll have to go back to Flash and output it larger.
Or, if you don’t have the original fla, you could click the swf, opening the Flash Player, and View>Full Screen (Ctrl F), to get a full screen viewing of the swf, then do a screen capture with someting like Camtasia Studio. It wouldn’t be a vector then either, but it would be bigger and sharp.