Reehm furnace. What happens when flames come on then shuts off when blower starts running.

How long does the flame stay lit

I see this sort of thing happen when an older thermostat has a burned anticipator, thus being unable to withstand the current of the control circuit. Do the status LED(S) blink or flash a code when this occurs? If not, your problem may be similar.

It can be one of two things. A limit is being tripped and killing 24v to the gas valve and bringing on the blower or you have a crack or hole in your heat exchanger and when the blower kicks on it blows the flame away from the flame sensor. In any case it could be dangerous and you would want to get the system checked out.