I guess my own answer to the question would be: for any frequency of flipping, there will be one last flip before it can never flips again (because the next flip would be beyond the event horizon on flashlight's proper time). But the higher the frequency, the more it will take for you to observe the last flip. If there is no limit on how high that frequency can be, there is no upper limit on how long the last visible flip can take to happen.

Please correct me if I am wrong.

I guess my own answer to the question would be: for any frequency of flipping, there will be one last flip before it can never be observed again (because the next flip would be beyond the event horizon on flashlight's proper time). But the higher the frequency, the more it will take for you to observe the last flip. If there is no limit on how high that frequency can be, there is no upper limit on how long the last visible flip can take to happen.

Please correct me if I am wrong.