Hi Ian, welcome to GoY.
no cutting the flowers off generally wont make a tree taller. You may get more leaves but it will depend on which tree you are talking about. To make plants bushier you need to prune out the leading growing tips but again depends on which tree you mean.

And if you pinch out the growing tip of the leader ie the middle shoot that will form the main trunk, it will affect the shape of the tree so please tell us exactly what you want to do, what the tree is and how long its been planted. A photo might help too.

What types of trees do you have in mind? You see, doing that to an apple tree would be disasterous and doing that to a 20 year old ornamental pear tree would be an impossible undertaking.