Don Knotts was a chain smoker at the time. It was odd to see him smoke on screen though. He and / or Andy decided early on that it wasn't a good form to light up on camera, so even though they both smoked off camera, you seldom see them do it on TAGS. Back in that day smoking was just beginning to be seen as a cause of lung and other cancers.
Yes, at the time it was seen as an ice breaker when meeting women in bars to have a lighter at the ready for when a woman pulled out a cigarette. My aunt, a smoker, taught me that at a fairly young age. Much to the perturbation of my mother who was not a smoker. Neither of my folks ever smoked, neither have I. There were times I heard my dad say, when offered a cigarette, "No thanks, I'm not old enough to start." I've used that line numerous times in my life. The usual response from the smoker, "Man I wish I had the guts to say then years ago when I started."
Now-a-days, this is not a social norm to offer to share one's pack with someone when lighting up.
Interestingly, I remember The Flintstones having a Winston commercial at the beginng and / or end credits. There was quite a lot fo consternation that got this clip and sponsor removed from a children's show. You might still be able to see the Flintstones ad on YouTube. If memory serves me, both Fred and Wilma lit up a Winston.