The range of situations you would use that sentence in English is limited. As an example, you get flowers from someone you don't like and want to tell them "I will keep the flowers but you can go" then you could absolutely say "The flowers are welcome". If that holds in German, I do not know - reading other comments it seems it could be the same (as well as also stiff/somewhat antiquated).
"The flowers are welcoming" was wrong. So was "The flowers are appreciated."
"The flowers are welcome" makes absolutely zero sense in English, at least American; why it's the expected answer is beyond me. This phrase implies flowers are sapient and should feel at home where they are.
A better translation, assuming the original German is indeed accurate, would be "The flowers are appreciated," which is a bit of an uncommon and flowery (pardon the pun) way of saying things, but it happens.
If the intent of the German phrase was "the presence of the flowers make a welcoming environment" then the translation should be "the flowers are welcoming."
In defense of the phrase that was given to us, I think it was trying to envoke the idea that the flowers might not have been sincerely cherished, or hated, but instead welcomed as a friendly gift from a friend, random person, or loved one.
Indubitably, the phrase, at least in the American-English "dialect", might be grammatically correct, but nonsensical out of context, especially because, as you stated, it sounds like the phrase is implying that the flowers are sapient and act as how the average homosapien would.
But I take the miscellaneous context as implying the flowers are a gift from someone you either know or don't know (But then again, why would anyone take anything from an anonymous stranger that he/she doesn't know about?), with the gift envoking a neutral conscent, neither love or hate, from the receiver.
While I do agree that the phrase sounds absurd out of context in the American-English language, I'm just giving my bias on what this phrase is trying to imply, neither an agreement or a disagreement.
A German native speaking here:
Don't let duo bust your balls with this scentence. It's not very common in German to say this. So don't be upset about this strange sentence and just keep on enjoying the otherwise pretty profound German course. ;)
Grüße aus Bayern und Respekt an jeden der Deutsch als Fremdsprache lernt!
Native (UK) English speaker. The sentence makes sense but is certainly common. 'The flowers are welcome' as in standing at the door after what you said last night they are the only thing that is and don't think that is sll it will take to make amends. 'The flowers are welcoming' is not correct. That would make 'welcoming' an adjective. Are they nodding their heads enthusiastically?