Hey everyone! There seems to be a lot of confusion in general about bluffing/calling the river with hands that block the missed flush draw. So I'll share some ideas that I've gleaned from looking at various solver outputs--specifically in the triple barrel lines.

1. When triple barreling as the aggressor, we (usually) don't want to block the missed flushdraw.
This is the one that most people are familiar with. The defender is calling twice with lots of flushdraws, most of which are folding the river. Blocking these hands decreases our opponent's folding frequency, which is bad when we are bluffing.

That said, this is not a hard and fast rule. Solvers don't mind bluffing the river with low flushdraws sometimes, in spots where our opponent mostly has high flushdraws. This often happens when the defender is out of position and facing a large overbet on the turn.

2. As the caller facing a 3 barrel, we (usually) prefer having a flushdraw blocker.
This follows logically from (1). It is somewhat opponent dependent though: if your opponent is bad enough to bluff with most of his missed flushdraws, then it can certainly be bad to have the blocker. But it's safe to say that most good players should be giving up the majority of their missed flushdraws, making it good to have the flush blocker.

As with (1), the rank of the flush blocker matters as well. The nut blocker usually adds more EV to your bluffcatcher, because from the aggressor's perspective, the nut flushdraw is the hand that blocks the most folds. Whereas a low flush blocker might be neutral or even -EV.

As a final note, remember that frequency is always more important than blocker effects. If you're facing a 3x pot overbet, having bottom pair with an Ad kicker is not an excuse to mash call when diamonds miss. Yes your hand will probably be close to 0EV in theory, but you lose a ton of EV in practice if villain isn't bluffing enough. Overall calling/bluffing frequency > blockers always.

For a more visual explanation as well as some examples, you can check out this 3min video that I did:
Paradox of the Flush Draw Blocker