I guess it's useless to try and extrapolate, but the Glasgow filming (which seems to be for Indy but we're not 100% sure yet) appears to be set in NYC with a street parade going on.
If they're setting it in a real parade and not a fictional one, there were quite a few so it doesn't really lock down a date. If it's not just a Thanksgiving Day parade (so potentially any year!), significant ones may be:
Charles De Gaulle's visit or JFK's nomination parade, both 1960
The Yankess winning the league, 1961
John Glenn / Yankees winning the World Series 1962
Apollo 11 astronauts / Mets 1969
Those seem to be the ones on first glance which might make a movie scene nowadays, although perhaps I missed something. There were a few more:
https://en.wikipedia.org/wiki/List_of_ticker-tape_parades_in_New_York_City
Would the sports ones have all of the US flags out, considering they're local teams?
Personally, I think -if it isn't a fictional parade (which is very possible)- 1960 feels the most likely.