I don't think a partner needs permission to flirt, and if somebody flirts with me I don't worry if their spouse is OK with it unless it appears to be flirting with sexual intent. Now if you ARE talking blatant sexual flirting, that's something that should be discussed to know where you both stand on it. I wouldn't move from flirting to sexual innuendo without a heads up to my partner/s, and I want the same info in return. I imagine you were just fine with him flirting with swinging partners, and the real issue is that you want him to let her know that he's in an open relationship, the sooner the better.
Truth is if he doesn't tell her, and it turns out she was willing to date him thinking he's cheating, you're starting off thinking he's OK with dishonesty and dating people who don't respect you. It doesn't matter if it turns out she's fine with dating somebody who is in an open relationship and nothing would've happened, the perception will always be there that you aren't sure she's a trustworthy person.
My 2 cents, I'd reiterate why I am uncomfortable about this and ask him to mention it to her today.
Happiness will never come to those who fail to appreciate what they already have.