Does he recognize that she's flirting and has been off with you? I wouldn't see this as my issue to deal with tbh.
I kinda agree with the poster that said if she doesn't know if he's with someone, or doesn't think it's serious then that's probably why she's still contacting him in that manner.
If she does know, then SO would deal with it since she's saying this stuff directly to him. Especially with flirting.