I bet the rest of the Brooklyn Nets roster is now having some doubts against KD as he might be not reliable enough just like the last season where he carried most of the load that made the team cross the playoffs. A player requesting a trade is really bad sign if that player still ends up playing the same team next season because the demand has not been meet by other teams and that's the situation of the Nets now.
Kyrie on the other hand doesn't have any problem at all and actually he said that he will stay and play for the Nets even if KD is not around with them anymore.
I don't think it's doubt, it's more of the team losing their trust on KD already. It's a big let down to hear from him wanting a trade or having their coach fired. And there could be more locker room drama specially if there will be close call or if they choke a game.
I'm not sure of Kyrie as well, if I'm not mistaken, I have read that the Nets are also tired of his antics. So they might as well trade him before training camp starts.
His inability to trust his team is exactly what is going to make him not be able to perform as well as he should. I would say that there is going to be a gradual decline in his performance as a result of this. He probably won't try as hard as he did before, which means he won't do as well.
I really don’t think that either KD or Kyrie is moving anywhere.