Having said that, there are many types of pouring spouts & systems out there that won't pour unless you push a button, put the bottle through a ring etc. but most flair bartenders use regular pour spouts and if done correctly will not spill. No one said it was easy but there are a wide range of moves that vary from high risk of spillage to very low risk.

If you are spilling then you are most likely doing a flair bartender move that either .. 1) cannot be done with that amount of liquid in it ( you really have to know what's possible and this comes with experience 2) you're doing too many rotation moves together in a row so even if you did have a low enough liquid level for one or two moves .. after a few the liquid will start to " creep up " the bottle and increase the odds of you spilling.