Dandelion Wine

I agree, he's clearly referencing Ray Bradbury's "Dandelion Wine." In that story, dandelion wine is a metaphor for capturing all the joys of summer to take with you throughout the winter.

Summer days were just a magazine, a magazine A magazine

It seems here the author is talking wistfully of summer days in the past, (as in he can picture them but they're not what's happening in front of you, sort of like a magazine?)

Cutting grass for gasoline, for gasoline So I can see ya soon

Dandelions grow in the grass and you would cut them to make the wine, so I think this is saying he's trying to make this dandelion wine so he can re-experience those great summer days. (a metaphor for 'the good old days," or anytime in your life that was great) (gasoline refers to the wine, which gives him the the ability to 'travel' back to those days)

Fall swooned Left me drunk in a field Dandelion wine for a year

Fall comes after summer, so I believe here he's saying those great 'summer days' ended and he was left drunk, ie: lost and disoriented. He got 'drunk' on the dandelion wine, that he drank to re-experience those great summer days but it didn't really do him any good.

I think here he's also tapping into the theme of the "happiness machine" from the Bradbury's novel. In the novel, a character builds a machine that can show you amazing wonderful things, a sort of ideal, dream-world, that's designed to make you happy, but in reality, everyone who uses it becomes sad beacuse it's not real and despite all the amazing things they see they realize right away they will have to leave the machine and go back to their life. So here, the author's saying that using this 'dandelion wine' to travel back and re-experience the good old days is ultimately self-defeating, you're living i a dream world and not moving forward with your life.

And I packed up the dust Of all that I owned Handkerchief hung from a pole

I think this could be another reference to the novel. The character that makes the happiness machine ends up burning it and his whole garage down. Or, it oculd be a reference to him "packing up" all the stuff that's holding him back from the past, which can be refered to metaphorically as 'dust' because it's not actually real. Either way, these lines are saying the author has resolved to move on from the past. The handkerchief hung from a pole could be referencing a truce or surrender flag. He's saying he's given up on trying to re-live the good old days.

I rolled out the day that the apples fell

I understand this as referencing back to him being 'drunk' on the 'dandelion wine for a year,' so in the song, a whole year has past and fall has come again, (when the apples fall) but this time around, instead of wasting away his life trying to re-live the past, he's ready to "roll out," to move on and ahead with his life.