Deformable means that the shape of something can be changed into something else. For example, in topology, a coffee cup can be deformed into a torus. Note the Wikipedia article refers to this deformation as a homeomorphism. A torus cannot be deformed into a sphere, hence they are not homeomorphic.
Flexible means that a substance can be bent, for example an arm joint, or the handle on a briefcase. It would not be correct to say that a briefcase handle is deformable or that a dancer is deformable.
Definitions for deformable and flexible.