You would need to make sure that the flowers were not contaminated with pesticides or animal droppings. Besides, I don't have the proper equipment for wine-making.
During the era of Prohibition, according to language in the Volstead Act, it was still legal to "manufacture nonintoxicating cider and fruit juices exclusively for use in [one's] home." It was this loophole that enabled individuals to make fruit juice or cider, which would of course ferment under certain conditions.
I don't know whether Minnie or Will actually made dandelion wine with her recipe, but I remember Dad telling about how his dad used to make root beer. One time the pressure in a root beer bottle kept in the cellar made the bottle explode, startling the family with the loud noise. I imagine it must have been fun for a five-year-old boy in the 1920's to have a cold drink of homemade root beer on a hot summer day.
Below is a copy of Minnie's original recipe for dandelion wine; I haven't come across the root beer recipe yet. If you do try making your own wine from the recipe, be sure to follow Minnie's advice and not drink too much of the home brewed hootch!