This question is more towards the English language, so maybe the
requester of this word could explain what they were thinking.

What exactly does "Wince, Cringe, Flinch" mean? Also the added
definition on the wish list does not help me: "Reflexively recoil or
shrink away".

Where would I use this?

Sogh qIpmeH HoD, ghopDaj pepDI' HoD, mur Sogh.
When the captain raises his hand to hit the lieutenant, the lieutenant cringes.
That is, the lieutenant backs off slightly and scrunches up a bit, possibly lifting their hands a little to ward off the blow, an instinctive reaction to an impending attack.

Generally, cringing is negatively associated with cowardice, while flinching and wincing are more neutral, though they can still be negative if you flinch or wince at the wrong thing. Exception: you can cringe at something extremely embarrassing, and it's not considered a negative behavior. Flinching has more to do with instinctively trying to avoid a blow, while wincing is usually associated with your reaction to pain, whether physical or psychological.

Those are my associations with the words as a native speaker of American English.

-- 
SuStel
http://trimboli.name