First, let's find out
1] why "That IS NOT going to happen." is correct
FOR US TO KNOW
2] why "That WILL not going to happen." is grammatically incorrect.
EXAMPLE #1: "That is not going to happen."
Grammar points to remember:
1] "that": is a demonstrative pronoun in that sentence.
(It represents a thing/things, an event/events, or a situation/situations.)
2] "is": is a BE verb; "is not": is its negative counterpart.
(BE verbs show action or a state of being and it MUST match the subject of the sentence. Hence, using the be verb "is not" in that sentence is appropriate for the subject "that".)
3] "going to": used to express future time.
(It is commonly used when an action is already planned or definite.)
(It is also used as a prediction based on evidence that we see at the present time.)
4] "happen": a verb.
(It means to take place or occur.)
In example #1, the verb "BE" and "going to" were used together. Thus, it is considered a "BE going to construction". To make it work, here are the points that we have to consider:
1] the "BE verb" must be in the correct form to agree with subject (in example #1, the subject is "That" and the BE verb is "is not")
2] "going to" must be combined with the simple form of the verb (in this case, with the verb "happen").
THEREFORE, the sentence "That is not going to happen." is GRAMMATICALLY correct.
EXAMPLE #2: "That will not going to happen."
So, when do we use "will"?
We use "will" when we are:
1] volunteering to do something. (Don't worry. I'll do that later.)
2] deciding to do something. (I'll go to the airport after my class.)
3] forcing someone to do something. (You'll do it, or else...)
NOTE: Will is not used for fixed or scheduled plans/events.
So, considering the points given in example #1, example #2 is grammatically INCORRECT.
You can read more on this at: http://web2.uvcs.uvic.ca/courses/elc/studyzone/
You can also ask your English teacher to give you more examples.