These are some various allied types proudly showing off some flags they have captured...
The first two were taken in East Africa, not sure where the third one is from.
As you can see, these all have the arms of Savoy
with the crown.
However...
The caption for this photo says it was taken in Italian Libya in 1942.
So while I believe the official flag of the Kingdom of Italy at that time had the crest, it seems other versions were in use as well.