MIMF

I am thinking of buying some flush trim router bit. Should I use it with a table or no?

You can use it handheld as long as you keep the router base perpendicular to the surface you're flush trimming.

Yes I know I CAN...but what SHOULD I do?

What are you using it for?

Joshua, no one here would presume to tell you you SHOULD do this or that with no idea what you're trying to accomplish!
Best results with most things generally are got by holding both cutting tool & work firmly in place (eg in this case...router table, ....or williams jig which I use to flush trim top & back to sides etc). The farther you move away from this generality, the greater risk you accept, but sometimes you have no choice.

I'd agree with Barry that without knowing your usage, it's hard to determine what would be the "best" way. For templates, I prefer to have the bit table mounted, so that I can easily register the pilot on the bit with the template without much fuss; also you won't have to worry about the router tipping as you follow a narrow template. For other tasks it depends on what you want to do; some are easier and faster handheld, some are faster on a table.

Routing to a template (e.g. headstock or tailpiece), I use it in a table. For trimming an archtop back or top flush with sides, it gets mounted in a router in my binding-channel router jig ala Harry Fleishman (See old archives soon.)

I am newer to guitar building but experienced woodworker.
I have a small lighter trim router for working some things by hand and my 3.5 hp router mounted in the table.

There are times the table just doesn't lend it self to doing routes in wood not straight like a cabrio table leg but, even then I clamp the work so its steady and try to add wood as a way to extend the surface to the router I would even use an even lower powered and lighter weight Dremel tool to lower your risk of injury or screwing up an part that may be expensive to replace or time consuming to remake.

long winded way of say use the table when even possible.