How to implement a double buffer using an ARM Cortex M3
If that MCU has a DMA engine that can feed whatever peripheral interface is driving the screen, and a memory bus arbiter between that and the CPU, and sufficient bandwidth to keep the peripheral fed in the face of arbitration, then it should work.

You could program the DMA to output the displayed buffer (ie, by priming DMA from its base address), while using the processor to write to the other.

You may also want to see if you can program the DMA to blit from one buffer to the other when you need to copy between them.