This is one of those phrases where French uses avoir, but English uses to be: j'ai faim, j'ai chaud, etc. Literal translations would be I have hunger and I have warm, but they are incorrect, and DL is right to mark them as such.
If you want an idiomatic translation that uses "luck" as a noun, something you hear in English is "I am in luck". I don't know if DL will accept it, though.
It doesn't really sound that natural. It's not necessarily incorrect though, I guess.
"I've got luck", but let's not push Duolingo's translation engine too far ;)
If its a negative statement, you use de or d' on its own regardless of gender or whether it's singular or plural. The affirmative takes de with the definite article or the contraction of them depending on all of those things: de la, de l', du or des.
In another question I translated "he has no luck" with "il n'a pas de la chance" and it was marked wrong because of the "la" and now here it is this "la". What's up with that?
It has to do with positives and negatives. When you make the sentence negative, you drop the article.
"J'ai de la chance" and "Je n'ai pas de chance" are correct
Why would "I have luck" be incorrect? Don't discredit my literal translations, Duolingo!