Rates will go down. Certain loopholes will be elliminated. Taxes will go up for some wealthy taxpayers, like hedge fund traders, who enjoyed loopholes, and therefore paid an artificially low marginal rate.
It is possible to make millions and pay zero taxes due to certain loopholes. This is the result of corrupt politics and lobbyist influence peddling. This is what Trump means when he says some wealthy people will pay higher taxes.
It’s entirely possible that’s what he intends, but that’s not what he said, and it would have been a VERY simple thing to say, so I wonder why he did not say it.