Dunno if the chosen topic name is correct, but here's the deal:

Let's assume we're HU IP, 100bb eff. no history.

Hero has A2hh
Villain has XxXx

Flop is Kh8h3x

PotSize is 5bb

Villain bets 5bb

Villain offers Odds of 2:1

Hero can only win if he hits his flush, if he does he always wins and all outs are clean.

Hero has 9 Outs out of a total of 47 Cards, so his Odds of making his Flush OTT are approx. 4.2:1

Hero needs to win 2.2x of the flop investement to break even.

Turn is a Brick.

PotSize is 15bb, Villain bets 15bb. Again, odds are 2:1. 9 out of 46 cards make Hero the winning hand. Approx. 4.1:1 odds are needed, Hero needs to win 2.1x of the Turn invest OTR.

Is the conclusion correct, that Hero now needs to win (2.2x Flop Invest) + (2.1x River Invest) OTR, that his calls on both streets are break even or is there another way this has to be calculated?

The money put into the pot on the flop is just part of the pot on the turn. Whatever the direct+implied odds are on the turn will answer whether hero should put money into the pot on that street.

OP's example has villain making a pot size bet after the brick turn card is dealt, with hero having a flush draw. Thus, the decision point is whether hero calls, raises or folds on the turn. As OP correctly noted, hero is given pot odds of 2 to 1 which translates to a required equity of 33% to continue and his flush draw doesn’t give him that. As Robert suggested, an implied odds analysis is one way to consider calling and hoping for a hit and big win on the river.

What about a raise? Plusses: A meaningful raise may get villain to fold often enough to make up for the equity lack.

Minusses: Villain may not fold often enough thus adding to the negative EV.

A model I have incorporates a fold equity function dependent on villain’s risk/reward ratio, which is used to estimate fold equity. Assuming a 20% river hit and win with a flush, I evaluated this problem three ways assuming villain is tight, moderate or loose relative to his folding propensity.

Tight: Positive EV is gotten for a raise of at least 36 (Villain folds 79% of the time at minimum raise size)

Moderate: Positive EV for a raise of at least 49 (Villain folds 54% of the time)

Loose: Positive EV for a raise of at least 68 (Villain folds 30.5% of the time)

With a Calling Station, the effective stack is not large enough to achieve +EV; i.e. villain will not fold often enough to overcome the equity deficiency.

Of course these results depend on the fold equity function one uses. Mine have a “lazy S-shape” where small bets have limited fold equity, fe rises rapidly in the middle and levels-off for large risk vs. reward.

The point of this response is that one can do a relatively detailed EV analysis in helping to make bet decisions or, more likely, through hand history review, help to discover leaks and thereby improve one’s bet-decision strategy.

Here is an image of the EV analysis described above showing the fold equity functions

Yes it's like that when you win.. don't phukn jinx me pussee.