What transpired between Conte and Tottenham is not far from being fetched, I believe the management has been noticing his style against the team and was unbearable to them after he called his team selfish after a match. This, of course, can't be the only reason, the internal issues with the players and the management which are not obvious to the media must have added to it. And as for Kane, his transfer is long overdue, Tottenham is not a fitting club for his personality anymore.
This is well said. A coach wouldn't say what you just mentioned when there wasn't an issue already before that. But even if a coach fires some bullets against the team, sometimes that is necessary as well. I haven't seen the game or the situation when he said those words against his team about selfishness, but Tottenham had some games that were absolutely unacceptable. First the game against Newcastle and then also the game against Liverpool when they were 0-3 down after 15 minutes again. As a coach I would lose my mind when.
Regarding Kane you nailed it, the transfer is overdue. But to what club? I think Newcastle could be an interesting option for him since they are a team on the rise, could use his experience and they are ambitious to build a strong team over the next years. He could be the perfect leader for the project that is already going in the right direction.