There are a lot of things you can do in the arena to simulate being out on a trail ride. If the flag scared her, find a flag and desensitize her to it in the arena. Or use a tarp as a "flag". Can you flap the tarp next to her without her flinching? Can you wave the tarp above her head without her flinching? Other things that you can use for desensitizing are a bag of cans and hula hoops (with the noise rattlers inside).
A big thing that I do with all my horses is get them used to something around their legs. You can use a lead rope, plastic bag tied to a stick or even a tarp. Whatever you use, your horse should stand still with four feet on the ground...no kicking out or moving away from scary object. I go so far as to pick up my horse's legs with a lead rope and make them hold their leg out (in a relaxed manner) until I put it back down. Think of what normally happens if a horse gets their leg caught in some wire...they thrash and kick trying to get free, which is what worsens the damage. If you have conditioned your horse to give to pressure on all four legs, they will not try to thrash and kick their way free of whatever is tangled around their legs.
All of this work is first done with you on the ground. Eventually you'll do the same kind of things from the saddle.
I love doing desensitizing work with the horses. Use your imagination! (This is coming from a person who took her horse through a marching band - bass drums pounding and tubas blaring - just to see what he would do. Um....I had to stop him from banging on the drum with his nose, he loved that drum!)