I am trying to base a superpower around bio-kinetic metabolism where the user can not only generate a massive amount of kinetic energy but can also absorb a massive amount of kinetic energy. Is there a way that the power bio-kinetic metabolism can do this. Here is a link to a site that explains bio-kinetic metabolism.
Remember that "energy cannot be created nor destroyed, it can only be transformed".
To absorb kinectic energy, you need something to transfer that energy to you. In order to transform it into other forms, the collision must be inelastic. That is on you.
That energy will become heat/sound and deform the character. They will be able to spend that energy by reverting back to their original shape - just like a bow!
The boring answer is "no". Kinetic energy is just the energy of motion, so it can only be stored in a moving object such as a flywheel. Scale down the storage mechanism to cellular level and you're soon talking about molecular motion, which is just another word for heat. To turn heat back into macroscopic motion requires something like a steam engine. Unless you could get all your molecules to start moving in the same direction, but then you'd have to explain yourself to Boltzmann, and he was notoriously hard to reason with.
But then, who wants to be boring. Instead of storing energy as motion, store it as mechanical potential energy, i.e. tiny molecular springs. Then you can absorb external kinetic energy (a punch, a thrown ball, being hit by a bus...), store it in those springs and return is when needed in the form of muscle movement. This is essentially Renan's answer.
The fact is that inefficiencies on the molecular level would still produce a lot of waste heat and, in effect, cook your superhero. But, being a cool lady of a certain age, she will shrug that off as hot flashes and keep right on heroing.