Her resisting him is part of the game to him, possibly. Not that she should let him kiss her - you are right to have her handle it but give her more tools to use rather than letting her just say "I'll handle it." She needs to know what is appropriate for handling this.
Roleplay with her exactly what she will say and do next time he leans in for a kiss and repeat that roleplay. Ensure that she knows to be firm but not touch him in any way (push, shove, etc. or she will be the one in trouble) Turning away from him quickly and stepping away while putting her hands up in front of her are great. Raising her voice enough to really get his attention is OK too -- far too often we teach kids to be "good" by using those "indoor voices" and they then feel reluctant to speak loudly when something really warrants it, such as if someone is in their personal space repeatedly. You might let the teacher know you've done roleplays with your child and they include her walking away and speaking firmly and possibly loudly. "O, do NOT try to kiss me. You are not allowed. I do not like it and you are not allowed to do it. I am telling the teacher." And then she should do just that, as calmly as she can. If she can get the idea of "I have space around me that is MINE and you are in that space, so you need to move away right now," even better and she should say that. Very important idea for kids to start to learn.
Talk to her about how it's important that she remember the roleplay and use it. It seems you're concerned that she might react somehow that's not good -- you mention "That scares me a bit because with her, that [handliing it herself] could mean anything!" That is why it's especially important that you establish with her exactly what "handling it herself" means here, so that she does not swat at him or tease him or melt into tears or otherwise make things worse for both of them. You also mention that she "does not want to tell me what she is going to do." Not a great sign; you need to establish with her that she must tell you exactly what she's going to do, and she has to stick to the plan you both come up with here.
She will not have to fend him off all year. It is still very early. He will tire of the game soon if not by the time you read these posts. If one good step away/hands up/loud, firm voice doesn't get his attention, tel the teacher again that he's persisting but I can't see that going on for long. If she's just been shrinking away and shrieking, he's seeing that as playing around with him,, and it might give him a little shock the one time she acts more like an adult would -- being firm and turning but not running away, with "NO, you are not ALLOWED to do that" etc.
Added: Interesting to see the posts leaping straight to "he's a bully, inform the principal and parents." Of course this behavior has to stop and the parents need to get involved if it does not stop, but kids this age have a LOT less impulse control than even slightly older ones and it is normal for kids to do something annoying over and over. That is not an excuse for this boy persisting, but it does give a little perspective: Should he really be branded a sexual harasser in the first weeks of kindergarten? I like Dana's answer about how kids need firm reminders of limits and especially I like the idea of having an all-class talk (no names!) about keeping hands and lips to ourselves. If the school has a counselor, he or she should already be in the classroom monthly doing counseling lessons. You should ask the counselor to do one this week and focus on just that topic -- personal space and not touching etc. If the counselor doesn't already do such lessons in all classes as part of her job -- she should. It's standard here.