I downloaded some information on playing flush draws from one of the coaching sites. Here is an shortened version of the scenario:

Hero holds 65, villian has AA.

On a board of T327 villian bets pot. Hero does not have the necessary 33% equity to call.

Then comes the following:

"Because there is still river action to come we have implied odds in addition to our pot odds. It is clear what cards make our hand are we are unlikely to be beat when we improve. We are also likely to extract value when we improve."

That all makes sense, but how far should it be carried? After all, an OESD has only one less out than a flush draw, so should it be played the same way? How about two overcards? Some players that will almost always call with overcards, and they have only two less outs than the OESD.

How far does this logic extend?

Just use numbers and don't worry about "extending logic"

The math works just like normal pot odds, except instead of comparing pot : bet, you compare pot : total bet

If the pot is 100 and he bets 50, and you're going to fold the river if you miss, then you can only lose the $50 bet on the turn. If he will call, say, $50 more if you hit, then you will win the pot + $50 turn bet + $50 river bet, a total of $200.

Now you're risking $50 to win $200 and your effective pot odds are 200:50 or 4:1

If he'll call $100 on the river when you hit, then your effective odds are
(100 + 50 + 100 ) : 50 = 250:50

And so forth.

Luckily our opponents don't always have AA. Sometimes they're bluffing thus we have some pair outs as well vs most opponents.

Easy call on the turn with lots of strong outs.

It's turtles all the way down.
You need to consider which river cards will be best for you (in the scenario posted, an offsuit 4 would be great, since it will look like a blank to villain, but give you the nuts; the Ah would also be sweet because villain will make top set when you bink the flush) and work out how much money you think you can win when you hit those cards. We use the standard comparison of hand equity and pot odds to make the decision, except we look at implied odds, not just immediate odds. With 65hh on T327hh, then against AA specifically you've got 9 flush outs and 3 more fours as outs for 12 outs total. Bear in mind that the flush would be "obvious", so villain won't necessarily pay off in full if a heart comes. 54o (OESD) would only have 8 outs, so it's less likely to hit, but fairly likely to get paid off when it does. A gutshot like J9 is even less likely to hit (4 outs), but it's so well hidden that you're almost guaranteed to get paid when the river brings an 8. With KQ (2 overs), you're actually drawing dead, so peeling with overcards against AA specifically would be terrible.

An additional wrinkle, but something you should always consider when calling with a weak draw, is not just the implied odds of getting paid when you hit, but also the potential opportunity for you to make a successful bluff when you miss. Players will often call (float) on the flop with a weak hand like a gutshot or an overcard + backdoor flush draw not just because they might hit their gin card, but because they will often get a chance to steal the pot by bluffing. If everyone played NLH according to direct pot odds, you'd have to fold flush draws on the flop, because you often don't get the right price. No one folds draws on the flop. You call because you think you can win the pot often enough to break even whether you make your hand or not.

Breaking down the raw equity with realization factors against villains range (IP/OOP is important here) is how implied odds is turned into somewhat math instead of nonsense.

We have:

9 flush outs, 18% -> when we hit, how often villain bets, or can we bet and how much eq we actually have vs villains range when we hit. Lets say that we always have nuts when we hit flush and are IP and POT left and villain defends correctly so when we always hit we always get chips in to the middle and villain calls 50% of his range, R = 1.5. So our fixed flush eq is 27%.

And do the same for oesd outs and then to pair outs too. Obv the numbers etc here are generic, but this is the basic logic how you can calculate implied odds.