Rounder Flounder.
Fat Cat
fat gnat
daring herring
Fish Dish.
fat bat
fat cat
round hound, jolly collie
pale scale, pale tail
If it were a Hink-Pink, it could be "a thick brick." Actually, the question is about Hink-Pink according to the original source for the question which is a book for gifted students. The section of the book asks about both hink pink and hinky pinky, and the question is in the hink-pink category on the page.
fish wishStout troutbad-bass
Fat Splat.
fat cat