How long does it take for a mole to fall off after treating it with iodine tincture?

It probably wont. I have never heard of treating a mole with iodine tincture. Iodine is not toxic enough to cause sloughing of skin. Best to have it seen by a dermatologist.
Few days to a week. Be careful , somtimes those what you think are mole could be some else like skin cancer? Check with your dr?