Is Fluxx a game of skill or luck?
There's a modicum of skill involved.  You can do some things to increase the odds that random draws will go your way.  Any or all of these could be used to augment Basic Player's behavior.


Recognize that some keepers appear more often in goals.  Prioritize The Brain and generally anything to do with food.
Playing keepers toward the current goal is usually a waste of time, especially with lots of players.  The goal may change several times before your next turn.
Avoid Draw X rules when you don't have Play X to back it up.  Otherwise you hand all your opponents extra card draw before your next turn.  A fistful of cards increases your chances of going off on your next turn, but it does so for everybody at the table.  Risk/reward.
Play your cards in the proper order, e.g., by not reducing/trashing the current Play rule before you've played all your cards.
Hang on to cards like Let's Do That Again and Take Another Turn until the board has some favorable Draw and Play rules.  Setting up a Dominion-style 5-minute turn is soooo much fun.


Ultimately, Fluxx is a fun game because of the crazy combinations that make everyone's heads spin.  Actively trying to win is of lesser importance.  In my opinion, the better skill to master is to make sure you don't make the game boring for everyone else:


Hand Limit 0 is an awesome card, provided you still have plays left for yourself to change it before your turn ends.  Draw 1/Play 1 with 0-card hands is painful.
Play All with Draw 1 is similarly bad, though it gets less painful with more opponents.