It's probably be stupid/bad for Trump to do this, but the anguished screams about the norm fairy are worse. Elected leaders should control government policy.
And yes, Trump has the authority to do this. Fed board members have been breaking a very simple law forever. 
I'm not a 'low interest rates are the best' type bc I think the in a deregulated financial world we actually deliver high rates to the poor while low rates are used for M&A. But if you're going to say Janet Yellen was The Best Chair Ever you should cheer for Trump firing Powell.
I also think it would be funny if Trump took advantage of an old conflict of interest law saying Fed board members can't own bank stocks (though they all do through index funds) to fire a guy he doesn't like. Ethics!
Think ahead. The Fed will be the first institution ready to kneecap the Dem President in 2021 when that President is like 'hey let's spend some money trying to deal with climate change.' The deficit will become the most important thing in the world say the oracles at the Fed.
