If a guy adds you on Facebook but doesn't give you his phone number, and when you try to voice call him on Facebook he doesn't respond is that a red

Lol not everyone wants to be called right away

Some poeple are not comfortable on calls and that too after two three chats.

Lots and Lots of scammers out there trying to steal your information. They friend you and as soon as you accept, they note all your friends, and download all of your pictures. They can then impersonate you and send friend requests to all your friends and continue collecting identities.
Be careful who you friend.

I would think it would be a red flag if you were trying to get to know each other on a romantic side of things, yes.

The red flag was a stranger adding you in the first place, forget the phone number.

I'm not interested in talking through those modalities

Face to face communication is king

Did y'all exchange messages first or did you just call him?

Women send me requests on Facebook and I completely ignore them

Yeah.

Way too many unknown elements to speculate on this one. Talk through messages and work up to arranging the voice call. People rarely answer unplanned calls these days. But if he doesn't want to plan a call, that could be a bad sign.