“Gonna” is a contraction of “going to”, and is considered to be colloquial English, to be used in informal contexts.
More formal situations, especially when writing, call for either “will” or (slightly less formally) “going to”.
As such, grammatical rules around the use of “gonna” will tend to be looser.
Having said that, “I’m gonna [do x]” is the most commonly used construction. “I am gonna” sounds a bit odd, since you’re combining the uncontracted “I am” with the contracted “gonna”. “I will gonna” would be considered wrong, since you wouldn’t say “I will going to [do x]”. You either say “I will [do x]” or “I’m/ I am going to [do x]”.
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