Bills is pwacticalictally Chargers! 
No, I mean, I was conflating the Bills with the Patriots. Same geographical region, same division, similar level of importance before the Tom Brady era, same washed-up-Flutie-versus-hot-young-phenom drama.
Still not sure how conflating the Bills with the Patriots results in you thinking Flutie was with the Chargers when he kicked it, but oh well. 
I knew it was after he was with the Bills. When someone said it happened while he was with the Patriots, I conflated the Bills with the Patriots and thought, “No, it was definitely after that.”
I have a feeling that not icing the kicker would have more of a psychological impact nowadays, since the kicker is so used to expecting it.
A point that could use some noting (well, stressing, if it’s been made already) is that in football, the conditions play a huge role in a successful kick. It’s more than just “getting a second chance at it”. On your second chance, you actually have more information than the first. Mostly, how much of an effect the wind will have on the kick and you can compensate for it.
Read the Esquire article on icing the kicker: