Yes it's correct. E.g. "I've started stretching every night before bed because I want to increase my flexibility".

As Richard S says, suppleness (bendability) and agility (grace and swiftness), are better words to use to refer to physical characteristics. While flexibility is a physical property, used to describe materials, if you describe a person as flexible we would automatically interpret the term in a different way. If you say, 'Emma is very flexible' most people would understand this to mean - particularly in a work context - that she is willing and able to alter her schedule, work different hours and days, and so on.

Flexibility is the ability to bend. Suppleness is another word that also means ability to bend. Agility is the ability to be quick and graceful. You might have agility on the basketball court or in the courtroom, or even with your gaming remote. The noun agility can be used for both mental and physical skills in speed and grace.