FLA is a file extension for macromedia flash MX... so you can use that program to edit the .fla file.
You did state paid right? You can purchase the program (very pricey if you are not going to use it for other projects.. or even profit off it). If they're just little changes, it's probably cheaper to just hire a graphics designer to edit it for you (most likely they'll have the program if they have flash skills)
Go to adobe.com and download the free trial version of flash, you can try it for 30 days, if you like it, buy it.
What are you trying to do with the .fla? If it's something simple, you could post the fla on DP and ask someone to edit it for you.