So gonna is not "proper" but is it technically wrong? When you speak properly could you say gonna or not?
In writing you should always write "going to", unless you are writing dialogue and want to indicate the particular way that a person speaks.
In speech in the American dialect, it is generally quite acceptable to pronounce "going to" so it sounds like "gonna" when forming the "going to" future.
I'm gonna eat some chicken. (okay)
I'm gonna the shops (Not okay)
When speaking carefully you don't make these contractions. It sounds unnatural to carefully say "gonna". If you are thinking about it, you should say "going to".
There are many many other similar short pronunciations and they vary from dialect to dialect. For example, in British English, the letter "t" is often dropped and replaced by a "glottal". Most of them are never written in speech. We might say "Hiiz gota lota bo'le" but we wouldn't try to spell it that way.