By "clues", do you mean a way to tell which English verbs are reflexive in French? Not really. Perhaps if you think of reciprocal or reflexive actions in English, you'd get somewhere, but no guarantees. For example, "se téléphoner" (to call each other) and "s'asseoir" (to sit yourself down) would be fairly obvious reflexive verbs.
The verb "se méfier de" is a particular instance of an "idiomatic" reflexive verb, because the word "méfier" only exists in this reflexive form and its meaning is idiomatic, as opposed to reflexive or reciprocal.
If your question is about grammar, then studying the rule for reflexives is quite an extensive topic, but there are plenty of resources online to get you going.
- Elle se méfie de son médecin à lui.
The subject will give you an obvious clue to which possessive is used, but using "his" is technically still valid, you'd just have to clarify in a real conversation. I don't guarantee that Duolingo will accept both all the time.