The only word you need to change is "increase". "I want to improve my English speaking ability." A couple of other things... Don't ever use "wanna" in regular writing. It's the most obvious way of showing that you are a non-native speaker. Look at how native English speakers write on italki, and you'll see we simply don't use "wanna"! :) Also, the verb "to be" takes adjectives, not adverbs. "Be correct", and "say correctly".

Hi, what would be the right way to say, "I want to be able to speak English better"?

I want to improve my ability to communicate verbally in English.

You can say (I want to improve my english)

I wanna improve my oral English.