I've never used the term myself, but I do find the idea of someone being offended by it a little humourous. The overuse of "cuck" is annoying though.
Basically, calling a millennial a snowflake is like calling any conservative a Nazi. It's an exaggeration of facts that pisses off anybody who it's used against, which is precisely why it's used in that context.
Calling someone a snowflake is just a sign that you are some loser who gets his identity from 4Chan and Breitbart.