Burke, though he nowhere mentions the American Revolution in the Reflections, had fifteen years earlier been sympathetic (very publicly) to the colonists. This did not, however, mean that he wished the colonies to become independent, as they eventually did. He and others in the Whig party believed the colonists's rights as Englishmen had been violated. Thus, their rebellion against the Crown was in some sense justified. The solution, in Burke's view, was for the King and his administration to make concessions to the Americans, which, of course, never happened, and the result was the independence of the United States.
Even with the resulting independence, this type of revolution was, in Burke's and others' eyes, totally different from the overthrow of the existing order in a settled European state like France. Perhaps this is one reason Burke does not allude to the American Revolutionary War in the Reflections. The type of revolution in Europe Burke did regard with approval was the 1688 "Glorious Revolution" in England, for it was a reaction against the alleged tyranny of James II and the violation of traditional English rights the anti-Stuart faction saw in the king's reign. As with the Americans 90 years later, a "revolution" was one in which natural rights established through tradition were restored, and this is the only legitimate type of revolt, in Burke's view.
Burke saw no such situation in France. To him, Louis XVI was a mild and reasonable monarch. Burke admired Marie Antoinette as well and spoke of her in glowing terms. Every aspect of the French Revolution, which at this point (in 1790) had not yet really turned violent, was condemned by Burke until in the closing pages of his book, where he seems to admit it is possible that some good might emerge, if only by chance, when there is a complete overthrow of an existing system.