That really depends on the tournament stage, stack sizes, ranges of your opponents and what the flop texture is.
betting out on the flop is fine if you think you are ahead, you just have to realise that your opponents will only call with a legitimate hand or draw. So you are unlikely to get value from most weaker (lets knock out the short stack type)
hands, and you will have to tighten the range you put them on, as they have to beat two hands at showdown rather than 1.
If the all in pot is negligible compared to the effective stack size of remaining players in the hand, then by all means play the hand aggressively as you normally would, just be aware that their checking may be implicit collusion rather than weakness.
lowering the chance of the all in player being eliminated by forcing other hands to fold, has ICM considerations near the bubble or in ITM
In my somewhat limited experience i find that players that have the intention of checking down will abandon that plan once one bet postflop has been made. Its like you break the truce to eliminate the other player by betting into a dry sidepot. So don't bet marginal hands.
And obviously don't bet drawing hands yourself as you would otherwise be seeing free cards, and missing would triple/quad up the short stack fi everyone else folded to your bets.
Feel free to point out any problems in my thinking