Make sure you horse is okay with a rodeo environment. There will be sponsor banners on the fence, flapping in the wind. There will be roughstock loaded into the chutes, making noise. There will be blaring music from speakers. And there will be lots of noise and cheers from the fans.
A LOT of stimulation. Is your horse going to be able to handle that? If not, start hauling him places now and work on desensitizing. You'll never be able to control your horse while holding a flag if he starts to panic.
And make sure you make a flag to practice at home with first. Just go buy a closet dowell and staple some noisy swishy fabric on it. Done! You've got a full size flag. Usually it's more the noise that scares most horses, than the flag itself. Have someone practice handing it to you, and taking it from you so that your horse is okay with that.
Just about any saddle shop should have a flag boot you can buy. Don't try to run flags without one.
Your horse needs to have a really good neck rein on him. Leg cues are great and all, but when you've got a heavy flag in your flag boot on your stirrup in the wind, you can forget about using your right leg to cue your horse. It just doesn't work. The flag and flag boot pulls it away from the horse.
Always keep the flag perfectly up and down. If it is really windy, that will not be easy to do. Your right arm will be tired by the end of the night. (Because you always carry a flag on your right side.)
Arena set-ups will vary a little, but typically, you will always run counter-clockwise around the arena so that the sponsor flag is between you and the crowd. No one wants to see the rider anyway .....
Gotta make those sponsors happy! On that same token, do not let the sponsor flags touch the ground ever. The sponsors don't want their flags getting dirty. Take care of their stuff.
Make sure you use the FULL arena. Don't cut the corners. Make your horse go the entire perimeter of the arena (but of course watch out for people/guys standing in front of the chutes).
If you have the opportunity to carry your state flag or the American flag and there is an eagle on the top of the pole, always make sure that eagle is facing forward. Rule of thumb for American flag is NOT to go mach 10 around the arena, out of respect (at least that's what I was taught). Trotting or a slow lope is perfectly acceptable to present the colors.
If you are in the arena with a flag while the National Anthem is being place (and you aren't the one carrying the American flag), always tilt your flag forward so that that it is lower than the American flag.
Make sure you have bobby pins or hairspray to keep your hat on. You don't want to lose your hat in the arena because you do not have a free hand to grab it.
Carrying flags in a rodeo is a blast. Have fun!!!