The idea of your story is an interesting one - alien civilization with a fetishistic devotion to #earthculture investigates our planet on a mission to find our glorious leader Captain Kirk. Hmm... sounds a lot like Galaxy Quest. Your writing is mostly smooth, although you make a couple of odd choices (like not telling us the name/number of one of the main characters until page 5, or having a page-long paragraph on page 7). But there is one fatal flaw. Unlike Galaxy Quest, I just didn't find this funny. The jokes didn't land for me.