It's not going to run the latest Mac OS... I'm not sure if you're looking at a PPC-based iMac or Intel-based one -- the switch over was around then. And I'm not sure what version of Flash you are planning to use.
Whether it's PPC-based or Intel-based, make sure you know it will run the software you want. A PPC-based one will only run PPC-based software. An intel one will run both (though if you're only going to run PPC-based software, the PPC-based one will be a little bit better). Look up the latest OS that the machine can run and make sure you don't want to run any software that is too new for it.
Regarding Flash development, I used maxed out Intel-based 2006 MBP for some flash development from ~2007-2009, which is probably pretty comperable to the first intel-based iMacs. It was fine for some projects and excruciatingly slow to publish for others, forcing me to break up the project into multiple flas/swfs and dynamically load them -- not the end of the world, especially considering I'd usually have to break them into two parts anyway to have a nice loading screen -- but do you want to spend your time on that stuff or building your game? I can't remember the exact version of Flash I used but it was fairly current at the time, probably CS3.
(I wasn't quite sure what was the trigger for making it so slow. Something to do with the graphics and sound, but it wasn't simply a matter of how much grapgics and sound -- sometimes I had a lot of graphics and sound and it would publish quickly. Sometimes a medium amount and it would publish slowly. I have some ideas but never definitively ran it down because I upgraded to a fast i7-based 2009 iMac and never had to worry about it again.)
So from my perspective, no, that's not sufficient. These games weren't big -- just me and an artist providing some nice, but not extensive, graphics.
I think it would handle word processing fine, with, e.g., a version of Word from around that time.
I don't know about Final Cut Pro 7.