Vocab problem: 肥 vs 胖 vs 肥胖
Is this one of the cases where two characters just remove ambiguity?

Yes, Since each Chinese character has its own meaning or meanings. A single character, usually cannot clearly express a specific meaning, therefore two characters would combine into a specific word, and two words may combine into one specific phase.(see my other post How to determine if character can be used separetely?)
In the case of 肥 and 胖. both can be an adjective for &quot;fat&quot;, however 肥 also has other meanings:

肥 http://www.cantonese.sheik.co.uk/dictionary/characters/188/
[1] [adj] fat; plump; chubby | [antonym] 瘦
[2] [adj] greasy; oily; fatty
[3] [adj] fertile; rich; luxuriant
[4] [n] fertilizer; manure
[5] [adj] profitable; lucrative; affluent

Combine 肥 and 胖 into 肥胖 make it a specific term for &quot;fat /obese &quot;. Since it is a specific term, it is also more formal.
Beside being an adjective for &quot;fat&quot;,  肥胖 can also be a noun for &quot;obesity&quot;