You're partly right. I think it is a Winn-Dixie Grocery Store stamp, too, but the reference is not "Amish Dividend" but "CASH DIVIDEND" ... that was the name of their stamps. It was similar to trading stamps (i.e. same perforations as S&H Green Stamps) but instead of trading the stamps for premium gifts, it went toward discounts on food products carried at the store. The W-D brass at the time said that a survey showed that customers preferred discounted food items rather than other gifts (but who knows?)
Anyway, here's another form of the Winn-Dixie Stamps in red:

And a Florida newspaper article from 1982 promoting them to Seniors:

Now I don't know if this has anything to do with the stamps in question, but I found this old sign for sale on the internet:

I'm skeptical that it relates to the same promotion, as it seems as though it would be too old. Remember, Winn-Dixie at one point gave TV Stamps (Top Value) Stamps as a premium but did away with them in the late 1960s, I believe, presumably in deference to their own branded stamp: