Hello!
In general, cover letters for short stories are short and sweet. They might relay a little bit of information about why you are submitting or love the property, but should be no longer than a paragraph or two.
Here's an example of one I tend to use:
Hello,
My name is Bryan Young and I've been publishing stories professionally for the last two decades. My last novel is BattleTech: Without Question, an important novel in a licensed universe. I'm pleased to submit "STORY NAME" to you. It's about 5k words long and tells the story of QUICK ONE SENTENCE EXPLANATION. It involves X FACTION, as they navigate X REGION, in the X ERA.
I have revelant personal experience with the subject <insert the experience>. I'm looking forward to your response to the story!
Thanks so much!
Bryan
We asked Phil about this, too, who is the editor of Shrapnel and he said that sometimes he likes to see why people love BattleTech or how they got into it or that personal connection to the universe, but a bad cover letter isn't going to get a good story rejected any more than a good cover letter is going to get a bad story accepted.
So, make sure it has relevant information to the editor so they know who you are and which story is yours and then really focus on making the writing shine.
