so he chats online or flirts whatever with women and this doesn't bother you in the least. When you flirt or chat online with men it bothers him.
I don't see a double standard.. I see him saying 'when you do that, it makes me uncomfortable'.
Reverse the roles and see how it sits. If you don't mind him chatting, great! If he minds you chatting/flirting and you stop, great!
This is about swinging (I think) so No means No and that gets respected and doesn't have to be 'explained'... talking about it over time is a good thing, tho...but if what he's doing doesn't bother you, and what you are doing bothers him, you have to stop doing what bothers him. At least, in swinging
If it's not about abuse, power, control, anger, etc. etc. in the relationship and it IS about swinging...you stop doing what upsets him about it...then.... what's the problem?