Is it correct that you can't skim and plaster walls so the become flat again?

Skim plaster should only be 2-5mm thick, if the walls were that bad in first place it would have been better to remove existing plaster and start again or bond out wall straight before skim coat applied, both above options would significantly increase the cost of works. It comes down to what you asked of your plasterer and what they agreed to do

If they weren’t flat to start with then no needed to be bonded and you should have asked for that but if were flat sounds like he can’t plaster he’s just a spread

It’s not correct. You dub the wall out. For example if there is a section of wall dipped you fill this out with plaster and key it. Do this to all the set back patches then float the wall with roughing then skim it. Almost all walls especially old walls stripped of plaster are hap hazard and require this. So he is incorrect either by accident or design. This should be taken into consideration during pricing or if discovered after reprised before the work starts. If it’s an over skim a plasterer should know it should be straight and discuss this. Use carrier banding to fill hollows then skim. It costs more but your job as a plasterer is to find out first what the customer wants.

It all depends on the back ground . Walls will bow over time. To get them out I would have eather 1. Bonded the wall out finding the spots where it had bowed or 2. Stripped the wall to the original brick work and boarded it so it was really flat.