Rounder Flounder.
rounder flounder
frail whale
fat sprat
Fat Cat
fat gnat
daring herring
Fish Dish.
fat bat
fat cat
round hound, jolly collie
pale scale, pale tail
fish wishStout troutbad-bass
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.
Fat Splat.
fat cat