I'm looking to buy a '97 Sidekick Sport JX 4WD with 5 speed manual. It's 1,800 miles from me so I'd fly there and drive it home. Is it FLAT towable behind my RV?

You sure can.  I have been flat towing my 92 Kick for decades.  I welded a baseplate on the front and use a Harbor Freight Towbar among others, HF LED tow lights, NSA Ready Stop and Brake.  For years the Kick was so light I just had the Ready Stop.  I barely notice it is behind me.  Ignition in acc so the wheel turns and Transfer case in Neutral and 2nd gear for flat towing.     Have a fun trip.

I'm looking to buy a '97 Sidekick Sport JX 4WD with 5 speed manual. It's 1,800 miles from me so I'd fly there and drive it home. Is it FLAT towable behind my RV?

I'd answer that with a MAYBE.

The transfer case has a neutral position, BUT, the deciding factor is going to be the front freewheel hubs, if it has auto freewheel hubs, then no, if it has manual front freewheel hubs, or you swap the auto for manual, then yes.

As mentioned above, transfer case in neutral, transmission in second gear, stop every 200 miles and run the engine for a few minutes, with the transmission in second gear and the transfer case in neutral to circulate the oil in the transfer case.

Once again, excellent help guys... thank you!

-Eric