Group Investigation Associates, who created the flyer, was an anti-rightwing group in the 60’s (“Founded in 1964 as an information gathering and political research organization. Primary research subjects are neo-Nazi, fascsist, and racist groups.” –bio note from archival holdings at University of Kansas).
The “God, Family and Country Rally” was an annual gathering, usually around July 4, by the (right wing) John Birch Society.
I see no notice of a “Boston Sing Out” event, either in local Boston papers, nor Broadside of Boston (folk music mag) for July 1965. My reading of the flyer, “Watch and listen for G.I.A. mobile sound equipment” would lead me to believe it was more of small scale happening, perhaps with folksinger Mike Fairbanks performing live (or on tape), but I don’t see anything that leads me to believe Dylan and Phil were performing there (the flyer noting that Phil recorded Dylan’s Birch song – if he was performing in person I would think he’d be more likely to perform his own material, not contribute a recording separately). I don’t see any indication of Dylan performing in Boston in July 1965, nor am I aware of Phil doing so (he was scheduled to start a residency at the Foghorn in Baltimore on July 5, which doesn’t preclude him playing somewhere else the day before, simply no evidence of his having done so). I think if BD had been there it would have garnered at least some attention.
Absence of evidence is not proof of anything, of course, but my suspicion is that this was more by way of a (drive by?) protest of the John Birch rally, rather than a big event with Phil or Bob actually there (no articles I have found on the 1965 Birch rally mentions protests, again, that might not have been caught by the mainstream press and Group Investigation Associates do not seem to be too active with publications to get definitive info via that route (they had a newsletter, but I’m not finding any holding locations for 1965 issues, and they also put out a listing of addresses for right wing groups, so folks could investigate/infiltrate).