My furnace runs for a few min then flickers and shuts off and then the system recycles and it fires back up and the process repeats over and over and over etc....
I had a similar problem in which the furnace would start its pre-purge cycle, and then shut off. The root cause was a broken solder joint on the controller circuit board, which I was able to see with strong reading glasses, and later repair by myself.
Try wiggling the low voltage electrical cables when your furnace acts up. If you find an intermittent contact, it could be due to one or more broken solder joints.
That's what it's supposed to do. It heats until a "high" cut-out temp, and rests until a "low" cut-in temp. If it's colder outside, that will chill down your house much faster, it will hit the "cut-in" threshold much sooner, and cycle more often. So if it started doing this during the cold snap, that's why.
If the heater is working at its limits due to the cold snap, it will barely turn off before it starts up again. The fix is a bigger heater, or temporarily running additional heaters e.g. electric.
In some thermostats there is an adjustment for the "spread" between cut-in and cut-out. You could try increasing that.
Also, thermostats are sometimes in a bad location: either too close to the heater, or blasted by a hot-air vent or convection. They think the house has warmed up, so they cut out, which causes rapid cycling. That can be handled by moving furniture, closing or redirecting vents, putting a cover or shield around the thermostat (a piece of paper will suffice for experimentation) etc.