gizzard of fowl, honest, sincere
肫 centers on the idea of inner substance: the gizzard as a dense, honest organ, and by extension sincerity and straightforwardness.
肫 combines ⺼ (flesh) with 屯, which likely contributes the sound. The gizzard meaning comes from the flesh component, while the honest/sincere sense may be a borrowed usage.
The flesh component ⺼ suggests an internal organ. Picture a gizzard as the honest, hardworking part of a bird that grinds food sincerely.
For シュン, imagine a gizzard that is soon to be cooked: soon -> シュン, and the gizzard is the honest, sincere part of the meal.