There's no chances or there's no chance?

Zero/None is neither singular nor plural. And that's why it can be both grammatically.

I have zero dogs. I have one dog. I have one/two/three (etc) dogs. That's what's being referenced in the meme. "no" is different than "zero". The correct phrase would be "There's no chance"

“No chance” but “Zero chances”

No chance but zero chances lol We can say I’m taking no chances, which is a different expression

Sorry I meant "I have zero chance"or I have zero chances?

zeros

"No chance" in context means that there is not a chance (though this isn't referencing a countable number of individual chances I don't think - it may have originally). "No chances" in context means that the countable number of chances you get are zero. So it fits.

Grammatically any number that isn't 1 is plural that includes zero but I would say the usage is changing and it is becoming that zero is both. But if you take a language exam the safe bet is making zero plural

"No" is a negative modifier and not a number. "There is" implies a singular subject, so you would use the singular version of "chance" in that sentence. If you started with "There are," the correct form would be "chances." In neither case does the "no" have any bearing on which form of "chance" should be used.

It also happens in Portuguese, lol.

There are zero chances

Nobody is 3rd person singular Nobody knows where she lives But then Is nobody at home?

Both can be correct. “I had no chances to score” means I was continuously looking and never found an opportunity. “I had no chance to score” means there was one time I tried to score but it had no way of succeeding. 

Zero is not plural. Zero is the absence of an amount. He's out of line, and he's dead wrong. If you say you have zero chance(s), you're just saying there is no chance.