We would say 'he is having a casual flirtation with her'. Casual flirtation means he isn't serious, he is just enjoying talking to her, being in her company, saying flattering things to her, but he doesn't expect it to go beyond that, nor last for very long. You can say flirtation without casual. If we say 'he is flirting with her', it means that just now, for this moment, he is flirting with her - perhaps at a party, but it won't go on any longer than that. If he is 'having a flirtation', it suggests that it is going on for a longer period of time.

Is this a sentence you've written? If so, it's unnatural. Try to write the idea again (and forget about which preposition - that doesn't help). The phrases you wanted for your second question are "petting" and "physically intimate". You managed to describe the situation, but in a very strange way. Look up "flirtation" again and decide how physical the action is. That will give you your answer.