Cash or tourneys? I can advise on 6max cash.
This has alot to do with your table image, reads/stats on your opponents etc. but also flop texture. In your example (assuming <50nl 6max), that flop is not as bad as you think, Kx hands are not liking that ace and hands like AK/AQ/AJ are mostly raising preflop so really the Ax hands in their range are low/mid ones.
Against this range you have good fold equity and you have to show that you're not afraid to cbet the big hand you represented preflop. If you give up on every A high flop people will soon notice and run over you. Just think, that flop is just as scary to them as it is to you and there are ALOT of other hands in their range which will insta muck to a cbet on that board (pairs, suited connectors etc).
If you raised pf with something like

and the flop was

then I wouldn't want to cbet. That board hits a ton of hands, such as pairs, suited connectors, flush draws etc. In a 3way pot you have almost zero fold equity and are never in good shape.
Say you raise with the same hand and get a flop like

. That is an excellent flop to cbet as it is believable that you have a piece of it while at the same time it hits only a very small part of your opponents range. You have great fold equity in this case.
Obviously it's best to be heads up in these situations but you can still fire out in 3-way pots, just be a little more careful and do it less often.
Hope that makes some sense.