As a summary of the above comments as requested:
The following SO answer is applicable: How can I detect if Flash is installed and if not, display a hidden div that informs the user?
Especially the comments / discussion of the above question are useful. I only remember that when we have used a Flash check we had combined two checks for some reasons I cannot recall. This was prior the iPad age, nowadays I'd check against the common [x]Pads if these are among the target audience. Maybe you combine the Flash and Browser check, e.g. once you know the browser is SAFARI/iPad you know it is not supporting Flash.
Try to encapsulate the check so you can change / extend it if required (that was useful for us).