Translation:He never hurries, he takes his time.
Another French pronominal verb with an English reflexive verb equivalent.
"He never hurries himself, he takes his time."
The reflexive in English is almost never used and only to emphasize "himself". So it is really an emphatic form, rather than a reflexive form. You could try reporting it, but I really don't think it will pass for this verb.
I'm surprised that the phrase "sb take his/her time" has exact equivalent (word by word) in French.
“up” is unnecessary here. It is used in imperative form. “Hurry up! I’ve been waiting a long time.” It is a more emphatic form. If I am waiting with the person who just said that, I might say “He never hurries up.” I could then add the rest as a separate sentence. You could try reporting to see if Duolingo will add it or not. I personally find it a bit much in that long sentence.
I wrote the same answer and resorted to my dictionary after I got rejected. As the comment above says, hurry up is in most cases only used in imperative form. Sometimes Duo gives me pain as a non-native English speaker...