Step 1: Link the clinical clue to the chemistry. A fishy smell from the body points to excess trimethylamine, a volatile amine that is normally detoxified by oxidation.
Step 2: The detoxifying enzyme is hepatic flavin-containing monooxygenase 3 (FMO3). The word $flavin$ is the key: this enzyme uses flavin cofactors ($FAD$ and $FMN$) which the body builds only from dietary riboflavin.
Step 3: Therefore a shortage of riboflavin starves FMO3 of its cofactor, trimethylamine piles up, and it escapes in urine and sweat as a fishy odour. Clinically, riboflavin is even prescribed to boost leftover FMO3 activity.
Step 4: Rule out the rest. Biotin is a carboxylase cofactor, thiamine drives carbohydrate metabolism, and vitamin A is needed for vision - none of these feeds the FMO3 reaction, so none explains the smell.
\[\boxed{\text{Riboflavin}}\]