I can't help but think that this is all a big con. Kelly asks Trump a question about his sexism, and Trump thinks he is getting rough treatment. Trump goes all in the next day calling Kelly a "bimbo" on Twitter. My suspicions are raised that this pissing contest is all for TV ratings because Kelly has an atrocious history of handling news stories with regards to race. See here and here.
Given Kelly's propaganda on racial matters, she should be giving a bear hug to Trump. A few of her fellow travelers in the world of journalism - I use that term loosely - have given Kelly good marks on a couple of occasions: confronting Rove during election night of 2012 and asking Chris Christie about his shitty poll ratings in NJ. Those stories, however, always struck me as the equivalent of stumbling over a big log in an old growth forest.
I suspect there may be some more negative coverage of Trump by Kelly. But I don't think that the negative coverage will cover anything truly damaging to Trump, at least not to the old white conservative men who think Trump is great. Ailes will also curtail any serious negative stories on Trump, and Kelly, as with the others on Fox, will do what the boss wants.