I think the baseline factor in determining a dynasty has to be titles, because, in my mind at least, "dynasty" connotes being No. 1.
The Bills made it to four straight Super Bowls but lost all four, so they were a very good team during that stretch, but not once did they prove themselves the best, so that can't be a dynasty period.
And even in the age of free agency, where things change a lot and often, I still think there has to be at least three titles in order to be a dynasty—that could be three straight titles, or three titles in, say, four or five years.
So even with a Chiefs win this week, they won't be a dynasty, IMO. I'd call them a mini-dynasty, with the potential to achieve "dynasty" status in the next couple years.