Hi J Keef. It sounds like a possibility may be a loose ground wire or ground path (I know you checked the wiring, but bear with me). From what you are describing it sounds like the gas valve could be cycling rapidly in response to loss of signal from the Flame detector. From what I understand, the flame detector (if it's the rod type) uses the gas flame itself to act as a rectifier; it is fed ac and the flame causes there to be a pulsing DC output that the control board senses. Because there is only one wire to the flame detector, it is merely an electrode; the current actually flows from the electrode ***through*** the flame to the parts of the furnace (FAU) that the flame touches. So the ground wire that connects the control board to the frame of the FAU is part of that control circuit. The current flow is in microamperes.
I'm wondering if there are thermal expansion changes that occur as the unit heats up that cause the ground path to become more firmly established once the unit warms up. The fact that it starts working staedily after a time makes me think less about the control board and more about something external to it. Also the blinking light would fit with a weak flame signal which would be caused by a poor or slightly intermittent connection (mimicking a weak flame that is flickering a bit). The other thing is (what I gather to be) the repeated occurrence of this and usually when first starting, not when it has been running. I wonder if some part of the heat exchanger flame tube or the like could be loose since the current must flow from the places that the flame touches. It gets hot and tightens up.