Sure there are parallels, although less acute now than, say, a month or two ago. For example, Leave might not have been expected to win, but for much of the lead-up to the vote the two sides were within margin of error of each other so only a stats novice (like, I suppose, David Cameron) would have been confident of a victory for Remain based on polling. Right now, in the polls, Trump is trailing by an ever-increasing margin, although with three months left there is still time for these trends to reverse.
The success of Brexit here has, I think, given any Trump supporters who were paying attention some hope. His opponents would do equally well to notice. They have the time to react, at least.