"I have no milk" is not accepted
It definitely should be. Added.
Is 'mleka' because is a negative sentence?
Yes, as is the rule, direct object is marked by accusative in positive statements and by genitive in negations:
"I haven't any milk" shouldn't be marked incorrect.
What about "I don't have milk" ?
Well, that's the most logical, basic answer. If it was rejected, it clearly must have been a bug.
do not = don't is accepted automatically by the algorithm.
And perhaps..i don't have any milk.
It's accepted, it should have worked.
no newborn → no milk