Duolingo's suggested translation does not have that, but it is possible to put something else at the start of the sentence. This then pushes the subject (ich) to be after the verb:

Ich trinke normalerweise Kaffee mit Milch
Normalerweise trinke ich Kaffee mit Milch

The latter sentence emphasises normalerweise slightly more, as though you're about to say "...but this time I'll make an exception".

Both those phrasings should be accepted by Duolingo and are probably in the database already. If you made a mistake somehow, there's an even chance that Duo will suggest the second sentence to you instead, which may have led to the confusion.

I am confused by the assumption of the existing I in the middle of the sentence, which seems to me to be missing. Or to put it short:

Hä?

I want to know that too. Only I think it is spelt gewöhnlich.

I dont think normalerweise can go at the end like it does in english