Is it possible to use PIC10Fxx internal flash to store data between deep sleep?
What you need to look for is if the processor can perform reads and writes to its own flash. I don't know of all members of the PIC10Fxx family do, but according to this page (https://www.microchip.com/wwwproducts/en/PIC10F322) the PIC10F322 does. A bullet point on that page says "Flash Program Memory with self read/write capability". Additionally, this part also has a separate 128 bytes of "high endurance flash memory" specifically for non-volatile storage.

MCU vendors often have white papers or application notes for this sort of thing.