There's actually a formula for finding out how much your floor flexes. A certain amount is allowed. Most flexing floors can be helped, but not cured, by first laying a product commonly known as 'cement board'. (I just finished 160 square feet using a product called
Hardibacker) It is actually made of cement and designed specifically for this application. It may or may not help,... I would have a professional take a look at the situation. The flexing produces a movement and reuslts in
decoupling... the term used to describe the floor tiles and grout cracking due to such movement.
This site has a lot of information to help you make a decision:
http://www.johnbridge.com/serv02.htm