If jazz piano is what you truly want to play, then there are a few requirements. The first thing is that you need to learn some traditional, classical music. This is because the fundamentals for jazz is the same as classical piano. By learning a traditional, classical style of piano, you will get a thorough grounding in reading music, as well as learning the basics of the notes and timing. Granted that jazz music does have its own unique style and rhythms, which tend to be reasonably complex, but the basics are exactly the same as classical music.
So I would recommend finding a piano teacher that specifically teaches jazz music. I don’t believe that they are quite as common as classical teachers, however, they most definitely do exist. If you can’t find one locally, then you can probably find one somewhere that teaches through online platforms like zoom or skype.
As an alternative, you could learn classical piano for a while to learn the fundamentals, before focusing on jazz music. While some people learn jazz music from day 1, there are many jazz piano players that learned to play classical piano first.
If you are going to learn jazz piano, then you really do need to learn to read music because it will help you learn and fully understand all the chords that are used in jazz music. While I do believe it is in your best interest to learn to read the musical notation, I do believe it is possible to become somewhat proficient in playing jazz piano, if you can play be ear, therefore possibly negating the need to read music.
If you are going to play jazz piano, then you will need to learn to improvise, which is a skill that can be taught over time – it is not one of those skills that either you have it or you don’t. Not that I have checked, but there is probably a number of YouTube videos that can help you learn to improvise. Having a piano teacher that can teach you improvisation skills would actually be the best way to learn to improvise.
As a result of quite a lot of jazz using syncopated rhythms, it is important that you have a good sense of timing and rhythm when it comes to playing jazz. If you have a natural sense of timing and rhythm, you most certainly have and advantage over others who don’t. This doesn’t mean that you can’t learn to have a good sense of rhythm and timing, as really anything is teachable, if you are willing to learn.
Not that I have any statistics to back up my claim, but I do believe that learning to play jazz piano is the least popular genre when it comes to learning to play the piano. This doesn’t mean that it is any less valid than the other genres, it just means it’s different. If this is what you truly want to learn, then don’t let anyone dissuade you from what you really want to do.