I had an accident and the rental car had damages, flipped upside down.
I didn't have collision Insurance for the Rental car (New Chevy
Malibu). My question is can I buy that car from rental company instead
of paying the full price of the car as part of damages and don't even
have the car.

Probably not.  The rental co. would have to pay full price for a
replacement in this case.

You are responsible for the cost of the car less salvage.

If you have a personal auto policy on your own car it probably will
cover this accident.

You also want to check to see if the credit card you charged your
rental has rental car coverage, many preferred cards do.