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Yes, I trust my partner 100% and he trusts me. We both have no problem "flirting" with other people because we are so secure in our relationship. And when I say flirting, I don't mean disrespectfully either. Just because you're in a relationship doesn't mean you have to stop looking, flirting, or accept compliments from other people. I think it's only human to look and flirt a little. As long as they know you're just playing around and you don't string anyone along into thinking that you want to get laid.
I sense a lot of insecurity here. If your partner cheats and lies, you know she/he is not worth your time and whether you're attentive and giving your partner everything they need to be faithful, it doesn't matter because it's not you. It's the cheaters and liars that have a problem so sooner or later, they would've cheated on you or anyone else for that matter.
If I couldn't flirt, I'd feel dead, lol! Flirting is more or less harmless, imo. Some people can't handle it, though, due to insecurities. I can't say I've never cheated on a girlfriend before, but I can say that it's not worth it in the end.
If you 'love' someone cheating becomes an obsolete concept, but flirting remains fun...