For years off an on I have taught Elizabeth Tallent’s flash fiction “No One's a Mystery”, often as a first reading in Intro to Literature.
Here are some possible approaches to teaching it.
Exposition. Examine the first paragraph in detail. What can you learn about this story's situation? How does your perception expand as the story proceeds?
Economy of Expression and Description. Because short stories are condensed narratives, writers must use economy of expression to say or suggest a lot in a few words. As readers, we need to be aware of this and crack open the nut to get the goodies inside. For example, there's a gift given in this story: the five year diary. That object takes on a significance, does it not? Notice the description of the lock on the diary: "it didn't seem to want to work." You can read that quickly and take it literally for what it is, a cheap lock on the diary. But you can also take it metaphorically. You can connect it to a larger theme running through the story: just what does the future hold for this relationship? Judging by the quality of the lock on the diary that will record that history, it doesn't look good.
Revelation of character through words, appearance, and deeds. Notice how the writer reveals Jack's character. She does it through his dialogue (what he says and how he says it) and through description of his dress, his truck, his actions.
Intertextuality. Compare the Rosanne Cash song "No One's a Mystery" (written by John Hiatt) - another detail that tells you something about Jack's character, about his attitude towards people. The way to formulate a character analysis is to assemble all the details the story gives you and look for patterns or tendencies. I think you can find that with the character of Jack.
How much plot do you need for a short story? As far as the plot of this story, not a lot happens. We have the complication of the wife approaching from the other direction, the tension of the girl having to hide inside the truck, but after that passes, there's not much else that happens except for a conversation between the narrator and Jack. In this discussion they exchange possible futures -- what will their relationship be like in one, two, three, four, five years? If there's a central conflict in the story, it is the conflict between their visions for the future. Jack's vision is realistic, even pessimistic, which is consistent with his character. The narrator's vision is idealistic: they're in love, they'll stay in love, he'll divorce the wife, they'll get married, have kids, her baby's breath will smell like vanilla, etc.
Reader response. What is your emotional response to these characters? What do you think of them as people? Which of the possible futures do you think will occur? The answer to that question inevitably involves you as the reader, your imagination. Based on the evidence the story provides, you can make an educated guess. Doesn't your answer have something to do with your own philosophy: idealism vs. realism?
By exploring this very short fiction in depth, you can model any number of approaches to literary analysis and interpretation. It’s a great piece and fun to teach.