I'm sure a lot of other emotional complications would come into it, but at a basic level, if my boyfriend wanted to sleep with someone else it would be clear that he didn't feel the same way about me as I do about him. A relationship like that will never be a healthy one, so I would get out. The same thing goes for kissing and everything else - I wouldn't do it, and I'd expect him not to.
Mild flirting is fine as far as I'm concerned - you can't police your boyfriend's every move, and I wouldn't want him to stop me from talking to men in case it could be construed as flirting. But I do it a lot less than I used to, and I expect him to hold back a certain amount too. I loved being single and flirting with blokes, and I tone it down now to save hurting his feelings, so I expect him to make the same small sacrifice for me. If he was flirting with someone so much that people thought the other woman was his girlfriend, I'd have some harsh words with him.