Looney Labs' website contains the following (excerpted here; much longer there):
Q: Can I make copies of my home-brewed Fluxx (or Chrono, or Nano, etc.) deck to give free to my friends?
A: Short answer, NO.
Looney Labs is the exclusive publisher of games that use the Fluxx engine, for which privilege we pay royalties to designer Andrew Looney. Fluxx is our most important brand, and it is simply not in the best interests of Looney Labs to permit competing entities to distribute copies of a game based on Fluxx (no matter how small the production run nor how unique the theme) to others in the marketplace.
Obviously, if you use their Fluxx Blanxx templates to make your cards, then they can enforce that because those templates are copyrighted. But they don't say "not if you use our templates"; they just say "no". Does that carry any real legal weight, though? If you make cards from scratch without their templates, what claim do they have over them? Is the "Fluxx engine" actually something that needs to be licensed? The two things that come to my mind are copyrights and patents, but I'm under the impression that game mechanics aren't copyrightable, and the game was released in 1996, so even if it were validly patented, it would have expired by now.