Question! Which country are you from?
The only US bingo games I could find that fit the description are 3 machines and they were made in the 50s, but I could see him playing older machines in the 60s.
The machine that closely matches your description is Bally's 1959 Fun Way. It's a bingo machine that has a couple of flags in the brackground and the playfield has a broadway vibe to it.
https://www.ipdb.org/machine.cgi?id=971
The other 2 are titled Broadway. Both made by Bally, but one was made in 1951 and the other is made in 1954 respectively. No flags though.
https://www.ipdb.org/machine.cgi?id=381
https://www.ipdb.org/machine.cgi?id=382
Now, if you are not located in the US, then it's going to be challenging to track it down. There were many bingo machines made in Europe and Asia that are unaccounted for.