York Affinity 9.C gas furnace won't stay lit
The video indicates your furnace does the following:

Thermostat calls for heat (2 yellow lights blinking indicates this as per York fault codes)
Draft inducer starts (:00 in video)
After xx seconds of draft inducer running, the pressure switch is satisfied, the igniter starts to heat and gas valve opens (clicks at :35 in video)
The burner jets light ('whoosh' at :37 in video)
After a few seconds the igniter stops heating (click at :42)
Gas is cut off, killing flame (click at :46, no more 'whoosh')

In a normal scenario, the burner jets light sequentially, starting at the igniter side, progressing to the flame sensor on the opposite side. When the igniter stops heating, if the flame sensor senses flames, that means all jets lit and are still lit. If the flame sensor does not sense flames, it cuts the gas and starts over.
So we hear flames, why does the flame sensor does not sense them? Could be one of the following:
Flame sensor problems:

Flame sensor dirty, not heating enough to sense flames
Flame sensor dead, not signaling to control board
Flame sensor disconnected temporarily, like corroded contacts shorting and prevent any signal reaching control board

Gas jet only partially lighting:

One or more gas jets clogged in sequence preventing final jet with flame sensor from lighting (I have seen spiders build nests that clog jets)

You potentially can rule out partial lighting by running the furnace as in the video without the cover on and see if all of the heating tubes have flame and that the flame sensor is engulfed. If this is the case, then try cleaning your flame sensor, checking its electrical cable continuity or replacing it (likely &lt;$20).