Believe it or not the standard play for me in this spot, is to check with the intention of checkraising. Heres why, whenever I am specically in a 3 handed raised pot and I flop a calling hand and the raiser is directly on my right, I will always raise in an attemt to isolate the raiser. If I'm out of position I will checkraise, If I have position I will raise. Even with just a naked flushdraw my hand plays better Heads up then letting the middle guy stay in. This is so becuz if I can successfuly isolate the raiser, my hand has a better chance to win if I spike a pair, and my hand has a better chance of winning unimproved since if the raiser doesnt have a hand, he will usually fold the turn, And lastly, there is always a chance the raiser will have a hand like KK on that Ace high board, and make a bad fold.

Betting out the flop is wrong IMO becuz if I bet out the flop, I am giving the middle guy a good price to stay in the hand for just one small bet, and if the middle guy calls and the button calls, now I have to actually make a hand to win this pot, which is not my entire objective. The same problem arises from checking and calling.

In specifically 3 handed raised pot situations, whenever you have a calling hand I think it is always best to play your hand is such a way to get it Heads up as soon as possible. This usually means I will be raising or checkraising with my "calling hand" and even when this play doesnt work, I only lose one small bet since I had to call anyways, and there are so many times that extra small bet investment the win the whole pot, when I dont even have a hand, that is it easily worth it. Plus this play is obviously very deceptive, and can easily get opponents to play back at you in the future when you actually have a hand which makes poker fun.

Another strategy in 3 handed raised pots thats worth considering is to raise or checkraise without a calling hand if you think the raiser missed the flop. With no reads, I think this play is too dangerous and should rarely be utilized since if one of the two opponents calls, you will have no hand to fall back on and no outs to hit.

A great example of checkraising with a calling hand in a 3 handed raised pot can be found in the book "how good is your limit holdem?" by Byron Jacobs and Jim Brier, page 162.

Note: I said this is the standard line I usually take in these situations with no reads, there are always excecptions to this play, like If I strongly believed that someone else already had a strong hand, I would obvioulsy be less apt to play my calling hand aggressively.