Take it easy until the horse tells you that he is ready to go faster. Practice at home, at the lope. If your field is big enough to set up a barrel pattern in, it's probably big enough for him to gallop, once he's comfortable enough and balanced enough at a lope. He'll let you know when that is. Just be consistent with his queues, and he will get it. Also, don't practice so much that he becomes bored, break up barrel training with trail riding or working on something else, that way he is not doing the same thing day after day.
Also, spurs shouldn't be used for speed, but for an extension of your leg for queues, to pick up his shoulder or bend his rib cage. His speed will come when he is ready, and trying to get him to run before that point will sour him to barrels, and it's easier to train a horse, then to re-train a soured horse.