What's the best route, thru or around Ft Worth, for a little caravan of three RVs (Altus AFB & Lawton-Ft Sill) travelling SW Oklahoma thru Wichita Falls going to Galveston after Christmas?

Not to put words in anyone's mouth, looking at the map looks like I-820 west of Ft Worth might be the best way if it's not consistently jammed like US-287 thru Ft Worth always has been in the past.

Try to hit FtWorth between 10am and 2pm. Follow the traffic app on your phone.

i would cut over to Bush Turnpike over in the Texas Motor Speedway area
You are aiming to I-45 I would guess

Most times of the year it makes sense to plan more, but the week between Christmas and New Years I would just keep an eye on Google Maps with traffic turned on and play it by ear.

287 is not all that bad if you can get it before or after rush traffic.
Where 287 and I20 meet has been and will be slow due to constuction and 287 is normally slow until you get to Midlothian.

If you aren't going through during rush hour its not too bad but if you are there are no good ways to go.

I RV also and I try to avoid large cities. I like the two lane roads. Look at 281 from Wichita Falls to Hico and then to Waco. Look at 36 down to Freeport. Along the coast to Galveston. This way isn't the fastest or the straightest, but it would keep you out of Fort Worth and Houston. Off of 45. Check the progress on the 45 rebuild south of Houston. It may be done. As I say I don't do interstates unless I have to.
By the way where in Galveston are you going?

287 South but not during rush hour p.m.

Like Morpheus said, but I would rather go through Gatesville and Temple instead of Waco.

Wichita Falls > Stephenville > Gatesville > Temple > Brenham > Rosenberg > West Columbia or Alvin (depending on where you're going in Galveston) > Galveston

You beat me to it. I’d go to Hamilton on 281 and then to Temple and then Brenham. Went this way with my camper and thru Alvin. Never had the Houston traffic.