Well, you can say this in Standard German, if you make a short pause between the two negations, such that the second nicht can be interpreted as part of the word nichtgehen which you won't find in any dictionary, but still will be understood as the opposite of gehen, i.e. as stay
Ich will nicht nicht-gehen.
I don't want to not-go.
But this is very unusual, and the chances that this will be understood are definitely lower than 100%.
But more common in German is to use a negation of a negated adjective.
Das ist nicht unüblich. = Das ist üblich.
The adjective üblich means common. You can invert the meaning of almost every adjective by adding the prefix un-.
You use the construction "nicht un-<adjective>" mainly if the negative adjective was expected, but it turns out, that in fact the positive is true. So, you think a young man is poor at playing the piano, but when you hear him playing, you realize, that he is talented. Then you say instead of »Er ist talentiert«:
Er ist nicht untalentiert.
The un- trick doesn't work with adverbs, because negating them doesn't make much sense (sehr, bald, montags, dort, daher, immerhin, also, doch, ...). The modal adverb gern is the only exception I know:
Ich mache das eigentlich gar nicht so ungern. = Ich mache das eigentlich ganz gern.
But almost all adjectives can also be used adverbial, and then you still can use un-:
Er bewegt sich nicht sehr unauffällig. = Er bewegt sich auffällig.
Beware also, that double negation can have the opposite effect in some German dialects like Bavarian:
Ich will gar nie nicht gehen.
The word gar is a modal particle, that best is translated by ignoring it. (Search for "modal particle" or "Modalpartikel" here on German.stackexchange to learn more about this) So, here is the word-by-word translation:
I want never not go.
This double negation is not understood as "I want to go", but as "I under no circumstances want to go." So, it is an enforcement of a negation. You stress out the negation by repeating it.