I guess "allowing flirting" is a turn of phrase that rubs me the wrong way. Is there a curfew and an allowance as well?
To add to what Red Pepper wrote about you having two girlfriends: It reads to me like you are on a power and possession trip. Your form of monogamy sounds like a design to control your partner. If you have two girlfriends, you are still in control. (They are both "faithful" to you).
You are in a relationship with a poly woman, man. You will not control her heart or eventually body. She will have to decide for herself and in her innermost heart what she can commit to and what she can't. One thing you can probably count on is 100% honesty if you let her be who she is.