Overall, I don't see any huge glaring issues, but the pictures are not that good.
Very hard to tell from the angle, but he may be a tad cow-hocked?
I don't know if posty is the word, but I would like to see his leg a little straighter under his hocks.
He's got a pretty steep shoulder angle.
Back is just a hair long (make it harder for them to collect ... but not impossible).
But he's sure got a nice hinny.
He looks decent enough for barrels anyway!
well he sure would be a flashy barrel racer and with barrel racing it honestly doesn't matter on conformation, so don't worry about it. Is he fast, does he neck rein, leg cues, stop, turn things like that are what need to be thought about.
Barrel racing is extremely strenuous on the joints and the body of the horse. If you aren't starting with a structurally sound horse in the first place, or a horse that has greater potential for weakness, you are increasing your risks of having the horse "not last" for their barrel racing career.
While yes, not all successful barrel racing horses have perfect conformation, I would pick the horse who is structurally sound over one that is not any day of the week. Yes, talent and heart are important. But if you horse falls apart because of lameness, that doesn't do you much good.