I don't think you understand what "friend zoning" is OP - it's not a problem, but you should be aware of it's meaning, as it comes across a little peculiar in this context.
"Friend zoning" is a term used by cretins who tend to follow the "pick up artist" code. The crux of it is that they "make friends" with women, and behave very nicely towards them, not because they have any interest in actually being friends, but because they believe (genuinely believe!) that if they are nice to a woman, and offer to do them small favours, then they are automatically owed sex by that woman. When the woman accepts their friendship, but rebuffs their (later) sexual advances, the man involved deems that she has unjustly "robbed" him of his right to have sex with her, and has maliciously put him in a "friend zone".
It's a very warped, and extremely bizarre view of the world, and not healthy.
If you are looking for a serious relationship, or just a relationship and want to see how it progresses, then take things slowly, but don't let yourself get strung along. If you want to go on a date with this person, just ask them on a date for god's sake. This is the 21st century - you shouldn't just be sat at home waiting for him to court you. Tell him you really enjoy your chats and would love to meet up for a coffee. If he says no, then forget about it.
If he says yes, then just see how you two click in person. If you get along, he should ask you out the next time, or you could invite him to a day showing at the cinema or something. The two rules I would say are:
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Don't get into a situation where one person is doing all the running. If you have invited him out two or three times, and he has asked you out zero, then he isn't interested. Then just quietly fade from contact. Don't chase him around. He will just take from that, that he is in a position of power and can pick you up and drop you as he likes.
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Don't invite him places, or go places early on, where it's an "evening event" - especially one with booze involved. It's basically just a lead in to sex. And if you aren't looking for a casual sex relationship then it's best to avoid until you have both seen each other a good number of times, and have an idea of whether he is interested in YOU or interested in anyone that is convenient for sex.