Whether your horse is kicking up to demonstrate his lack of respect or truly bucking out of fear or habit, there are several ways to fix the problem. If he’s kicking up because he doesn’t want to go forward (which is most often the case), go back and get his feet moving better on the ground.
Preferably, put him in a roundpen, and then point up in the air with your hand to signal him to move forward, cluck and spank – first spank the ground, and if necessary, spank him – until he lopes around the roundpen. Get him so hooked on you that as soon as you ask him to move by pointing with your hand, he immediately responds. If you get rid of his laziness and lack of respect on the ground first, when you get on him he’ll be a lot more willing to go forward. In fact, if you thoroughly do your groundwork, more than likely kicking up under saddle will no longer even be an issue.
When you do get on the horse and ask him to lope, first squeeze with both legs to ask him to go forward. Wait for a count of two, and if he doesn’t go, cluck. Wait for another count of two, and when he doesn’t go forward, spank him from side to side with the end of your mecate or a dressage whip. If you spank with rhythm and he kicks up with both his back legs, what do you do? You spank him again: WHACK, WHACK. You may have to spank him several times before he realizes that every time his hind legs leave the ground you will make him feel uncomfortable, but when he leaves his feet on the ground and goes forward, you will leave him alone.
I’ll be the first to tell you that you have to be a confident rider to go through this process. If you’re not, either make sure you do your groundwork thoroughly and correctly so that your horse will go forward as soon as you squeeze and cluck, or have a more experienced rider ride the horse for a few days to get his feet moving at the lope.