"I put flowers in the vase."
Eh, I'd agree but Duolingo makes heavy use of the English present simple to translate the same tense in other languages, even if present continuous would be more natural in English - it's their way of checking you can recognise and use the same tense in the other language
If you got a sentence like 昼ごはんを食べます you'd be expected to put "I eat lunch" and not "I am eating lunch" or "I am going to eat lunch". It's the same going the other way too, so in this environment you could interpret an ambiguous verb like put either way. They should definitely both be accepted
As usual, if you honestly think your translation is a valid one, report it! They add alternatives eventually
They may have to change this to "I have put flowers in the vase" to clarify. I know it implies the perfect aspect, which wouldn't be quite right either (in Japanese), but I can't think of another solution.
I was so geared to present tense, I couldn't even see the perfectly grammatical potential past tense in there. It's a hazard of these weird sample sentences with their plain present tense that nobody actually speaks in, you learn to look for slightly odd sentences and ignore more sensible ones.
Well, both で and に have more than one usage, and I suppose that in this sentence で would be interpreted as the instrumental case marker — as "I put flowers by means of the vase", or maybe in the same way it is in 食堂で寿司を食べました。="I ate sushi in the cafeteria": 食堂で does not literally mean "inside the cafeteria", で just marks 食堂 as a location where an action of a dynamic verb 食べる took place. That is, 花瓶で花を入れました。would mean that the vase was not a destination point for flowers, but a location where the action of putting flowers was performed, and this, in turn, would mean that "I" (the speaker who performed the action) was in the vase (just as "I" was in the cafeteria where "I" ate sushi).
But "I put flowers by means of the vase" would be like using the vase to transport the flowers in order to put them into something else. I think it's more "the end destination of the flowers is inside the vase" (which is why ni is used.)
It's the same idea as climbing the mountain. The action is being done to the mountain (ni) instead of the site of the climbing being at the mountain (de). Compare "I climbed up the mountain." vs "I climbed at the mountain."