I stumbled upon this clip.

I do not know the name of this movie.

Looks like it is from the 1960s.

https://youtu.be/EB1aPXogjs8

It's from Farz (1967), see e.g. here at 00:52:51 - https://www.youtube.com/watch?v=onO7URuLzzU

I love that scene - I'd stumbled on it some time ago but also never knew the name of the film. Just proves that pie fights are universal!

The Hannah Barbera sound effects are everything