Be careful where you share proprietary assets. I'd hesitate to share a FLA like that with a service.
Do note that from Flash CS5 and beyond the FLA is really a .zip file in disguise. If you make a copy of the FLA, rename it to yourFLA.zip and look inside you will find metadata info about the version and build of Flash that created the document. Unless the user saved down to a lower version it's a safe assumption the version of the software it mentions is what the FLA version is.
e.g. from a CS5.5 FLA in DOMDocuemnt.xml:
creatorInfo="Adobe Flash Professional CS5.5"
Again it doesn't guarantee that's the correct versin of the file but it lets you know what the max could be.
Thanks for the tip. FLAver is not a service however, it's just a local go-between when opening the file to automatically determine which version it is.
More info is given here: