Personally I feel that Asterion would avoid anything relating to bondage, chastity, or actions and fetishes otherwise relating to previous torture and abuse. Being sexually exposed to another person is a very vulnerable state, and my interpretation of Asterion views him as inexperienced at best. However, while Asterion can be shy, he also has moments of confidence and will even physically overpower the Master.
If Asterion were to flirt, I imagine him doing it through his poetry, getting ever-more erotic with his descriptions, but I wouldn't be surprised if he has little to no knowledge of current-day slang in relation to sex. It's hardly something I think guests would be openly talking about, but perhaps Luke would have taught him some things over time? Maybe Asterion would even end up teaching us, like the route with his project teaching us obscenities from the past.
For Master flirting, there's many opportunities to grab Asterion's tail already throughout the story, I wouldn't be surprised if that became their personal way of flirting and hinting at Asterion that it's time for a private moment in the bedroom. He gets bashful and shy when the Master grabs his tail, and it's been shown to happen with his horns too.
I'd very much like to see Asterion and Master in more of a playful relationship than a very serious one. The way Asterion bounces around happily like a calf when excited, and that smile, are some of the most warming parts of his character.
For fetishes, that is a difficult question on Asterion's side. As I mentioned, I doubt he would be into anything adjacent to things he has been tortured with in the past. But since he is forbidden from being naked around guests, it would be quite fun to have the Master declare Asterion as unable to wear clothes when in the Master's quarters, either as a nudge towards humiliation, exhibitionism, or the Master's own voyeurism. There's also a rather abundant use of scent-based commentary throughout the story, Asterion knows you love to smell him, perhaps that would be taken a step further, after a gym or swimming scene.
Overall, one scene I would definitely love to see between Master and Asterion is the two exploring each other's bodies. Asterion is forbidden from becoming intimate with guests, and it's very doubtful any Master in the past has allowed Asterion to see much of their body, let alone touch. He would certainly enjoy the opportunity to simply feel a human body, feel the Master. Realise that, despite his bullish features, parts of him are simply human. He isn't so different. He is normal, and healthy. It would be very reassuring to him.