Just my thoughts:
The flame gets passed on well ahead of the Patriarch, though. He continues to touch his candle to those who approach him, but the people who receive it are to pass it along to others in a chain.
As for washing their faces and hands in the flames, it can be done with any candle at any time and I have a beard. I do it at parties for fun, and can actually keep my hand over and in fires much longer than anyone has in any of the videos. Flame is not hot itself, but rather the air around it; if you keep your hand moving you can keep it in constant contact with the flame with only minimal warmth. I’ve turned my hands black with soot doing this before, and not so much as a minor burn.
In short, nothing reported about the properties of the flame are unique or special, but merely par for the course. As for the balls of light and such, the videos and photos that claim to show them are very inconclusive, and I’ve read reports from people who were right there in those years who say there was nothing spectacular occuring, just people passing candles as usual.
On a final note, if you read the older accounts of the miracle from centuries ago it was a much different event, with a cloud coming down into the church and lighting all the candles at once, nothing about “flames that don’t burn” being passed from candle to candle. My personal belief is that if the miracle did occur at one time, it no longer does; what is currently described as “the miracle” is not at all the same as it was during the time of the Crusades, and nothing miraculous is truly being described.
Peace and God bless!