If you knock it off the board when you opponent is not looking, I don't see how it can be traded.
How to avoid trading your fianchettoed bishop?

Is Bh8 (for example in the Dragon) generally considered to be strong? I recall a GM saying that it is one of the most overrated maneuvers as the bishop on h6 can be a real pain.

Jenium, that is correct. Creating the one zero effect (your opponent's bishop having a greater effect than yours) is no good. Better to allow exchange and then adapt to the circumstances. If there is exchange in the KID, try to put as many pawns as possible on the black squares and aim for the endgame where hopefully you will end up with a better bishop endgame. Old strategy but still works. The pawn strategy does not work in a Dragon, of course, because you have an open game.
I'm not a Kings Indian player, but the trade is usually better for Black than you think, since Black's pawns are often on the dark squares and White is not the one attacking the kingside. A lot of players (including myself) reflexively play Be3/Qd2 whenever they can, but don't automatically assume it is good!

In the classical KID, there is a line invented by Petrosian where black plays Bh6 to exchange his bishop for the one still asleep on c1.

"Usually in the King's Indian you're happy to trade of the darksquared bishop since it's blocked by a pawn on e5."
It's amazing how we can find different views on such subjects.
While your comment obviously contains some truth, I've read this one too :
One can ask why black plays e5, blocking their own bishop in g7. Well, it has a prophylactic effect : if white opens the center, thus freeing the e5 black pawn, then the g7 bishop will become a very strong piece.

Hi all, as black I play King's Indian a lot, and from time to time, white will get a bishop on the edge to attack my fianchettoed bishop, supported by his queen to force a trade. Any advice on how to not trade it off? Thanks.
There are times you want to trade off the bishop, and there are times you dont. Study the KID more and learn.

pfren, that is a non-answer unless you can be more specific for the benefit those here.
Despite general guidelines I think real chess is about exceptions. Chess demands specific attention to what is there.
Never the less, I contine myself with the notion that I can take "knowledge" to the board from previous stuying and "avoid" work when there. Human beings are lazy - we don't want to think !
Here's a postion from a game of mine last year.
After Qh5 Fritz suggest g4 or Bxf6 - I played neither. The latter is very surprising because white is giving up his dark square bishop for black's knight - this didn't even cross my mind for a nano second. Unusual and counter to usual norms. I believe exceptional players see exceptional moves.

Let opponent Bxg7 then you Kxg7 thus protecting the h6 square from Qh6 that can cause problems with the King on G8. Especially if opponent has a knight ready for f5 or g5 or the h rook on an open file.

jengiais, your answer translates to: it is pointless having a coach who can answer questions. Experienced coaches can set down guidelines as to when to allow the exchange, when to not. Then there will be the specifics of the position and therefore calculation. But at least the student has some idea of what he is doing when tackling the specific position.

Conzipe, your plan is not so straightforward. When white plays Nd5, black takes it with the bishop and then plays Nc5, perhaps with Qb6 first. White's only hope of counterplay is on the e file (white to recapture on d5 with ed). Black has play with a4. Black can also try Qb4 and the doubling of the pawns is good for black. Black can sometimes also get in e5 reposition his knight to d4 (if white not capture en passant).
Hi all, as black I play King's Indian a lot, and from time to time, white will get a bishop on the edge to attack my fianchettoed bishop, supported by his queen to force a trade. Any advice on how to not trade it off? Thanks.