-When he first takes an interest in you, no one knows but him. That's on purpose, of course, but he didn't realize it himself either until he felt those familiar feelings fluttering about in his chest. As much as he'd like to reject those emotions due to his complicated life situation, he can't deprive himself of happiness, and he has to admit talking to you does make him rather happy.
-His compliments are simple, along the lines of 'You look rather lovely today' and 'I always appreciate your company'. It could all sound like he's just being nice and polite, but it should be noted he doesn't say anything quite like that to anyone else.
-Now, once you're together officially is when he's more open with showing affection, knowing you return his feelings giving him the confidence to be bolder in what he says. His compliments are often more specific, mentioning a favorite shirt of yours that you happen to be wearing or talking about the fact your lips were looking irresistible that day.
-He may prefer to be more subtle when it comes to flirting, but it doesn't mean he doesn't know how to get his point across should you not be taking the hint. It would take him a little longer to get your attention, since he's not sure if you're just uninterested in him or if you're really oblivious, so he takes his time before making a bolder move.
-It's a little frustrating to him, of course, if he's so blatant and you still question him, but it's not as though he hasn't come across people like you in his previous lives. He will confess directly his interest in you and ask for a date, a romantic date in which he has romantic intentions, and will reassure you that his interest is, indeed, romantic in nature.