fhèin here means "-self", and like the use of -self in English, it emphasises the pronoun (or name) and goes straight after the pronoun that it refers to. Mi fhìn, thu fhèin, etc. Here the pronoun thu is curled up and hiding at the end of leat, but it's there nonetheless, so fhèin needs to follow immediately after leat.
Leat is an example of a prepositional pronoun - prepositional pronouns are a major feature of Gaelic, and Duolingo introduces them gradually. Basically they are a combination of a preposition plus a pronoun. le (with) + thu = leat. As mi needs fhìn rather than fhèin, you would change Is toil leam marag-dhubh to Is toil leam fhìn marag-dhubh if you wanted to change "I like black pudding" to "I myself like black pudding".
The same would apply to names rather than pronouns - an toil le Nebojshaki fhèin marag-dhubh?
Fhèin is not a reflexive pronoun here but an emphasizer. It has the same meaning and function as the emphatic suffixes -se, -sa, -e, -san, with the difference that fhèin immediately follows the pronoun, while the suffixes are attached to it. An toil leat fhèin marag-dhubh? = An toil leatsa marag-dhubh? Both could be translated as "do you yourself like black pudding?" or "do you like black pudding?" (but for Duolingo's purposes I recommend using "-self" for fhìn/fhèin, and the emphatic pronoun (which you can't show on Duolingo's answers) for -se, -sa, -e, -san).
I hope that helps!