I don't think Kennedy is going anywhere, though part of me wishes they would find a different steward. Financially, she has done very well by LucasFilm so far. 3 movies and only 1 a dud, huge profits overall. Not all movies are going to hit all the time. Disney knows this.
I do hope they yank the trilogy from Johnson. Though at least if he has a whole trilogy, and does all 3, it might hang together better than giving him the middle piece of someone else's trilogy. But I don't think he's going to lose the project so long as Episode IX does well. TLJ, for all the possible flaws we've discussed and argued about ad nauseum on this board, brought in a boat load of money.
I have to believe, though, that a lot for both Johnson and Kennedy's future at LucasFilm, is riding on Abrams. Episode IX has to do well. How we define "well" we can argue about in the future. But if it disappoints LucasFilm and Disney, then it is clear that a franchise that was riding high going into Johnson's piece came out bruised and battered, despite the money. Two disappointments in a row would be hard to excuse.
If Episode IX does well, as I suspect it will, then Solo was just a standalone mistake. No reflection on Johnson and a single mistake among 5 movies is a pretty good score for Kennedy. So I think we just have to wait until next Christmas...