Ich schlafe im Auto in meiner Pause.
is totally fine.
I really don't know, why Duolingo would flag it as wrong. You're right: there is nothing wrong with your word order since German is quite flexible with it.
Since some people called my answer wrong I want to elaborate a little:
There is a rule of thumb (as @RDBury stated in a comment). The TeKaMoLo/wann,warum,wie,wo rule (when - why - how - where). That's something to give a beginner orientation about what order would be right (or better: common) in most cases. Maybe Duolingo wanted you to follow this rule?
Usually you would deliberately trespass against it and put something in first (or sometimes even last position) for emphasis.
But consider the following dialog:
A and B meet at work in the morning.
A: Das Baby hat mich die ganze Nacht wach gehalten. Ich habe überhaupt nicht geschlafen.
The baby held me awake all night. I didn't sleep at all.
B: Ach du ...! Wie willst du denn 8 Stunden Arbeit durchstehen?
Damn! How do you want to get through 8 hours of work?
A: Ich schlafe im Auto in meiner Pause.
This is perfectly fine. There is no need to emphasize anything - neither place nor time. Maybe place came to A's mind first and then he wanted to add that he will sleep in his breaktime ... or whatever. There is absolutely nothing wrong with this sentence and it's not about emphasis.
Especially as a beginner: don't let people frustrate you by telling you that something is wrong with your grammar or your style or something because you didn't follow a (as @RDBury called it) paper rule! Language is for communication. You want other people to understand you, right!? In this case everyone will understand your sentence without any doubt.
If you ask me (as a native speaker) there is absolutely nothing wrong with your sentence - neither regarding grammar nor regarding style.