The parade is on June *25*.
http://www.ilga-europe.org/resources/pride-event-calendar/milano-pride
The parade leaves at the central station and goes through
https://en.wikipedia.org/wiki/Corso_Buenos_Aires (then you can go back
with tram 9) so it's rather easy to coordinate for a group arriving by
train.
This year celebrates
http://www.ilga-europe.org/resources/news/latest-news/italy-recognises-same…
The Milan pride is a rather institutional one, e.g. the mayor attends:
https://twitter.com/giulianopisapia/status/614828048920223745
Nemo