Not standard flashbacks, where you insert scenes from a time before the main body of the story, but I did use fragments of scenes from past times. I can't think of any better way to accomplish what I needed to do, but now I wish I'd tried a different approach altogether. Those fragments of flashback, I think, are what made me feel this story wasn't of a piece. Those fragments might as well have been stuck onto the rest of the story with that gummy plastic-y stuff people use to seal gaps in their shower tile.
If this hadn't been a short story, and a short story of under 2500 words at that, I might have shown the two characters having their relationship in sequence, perhaps showing them as they together invented the story's science fictional element, then moving on to the accident that befalls one of the characters, and their subsequent figuring out of a new use for their invention. That would have taken more wordcount, for sure, but it might have been better. I might have been more satisfied with it. Alternatively, readers might have been bored by so much setup before the "real" story began. No wonder writers are neurotic.
I ended up throwing character one, who's the first person narrator, and the sf element into the midst of the "real" story, or what I hope was the "real" story. As a consequence, character two was already incapacitated and could have no lines and could not move around himself to show his relationship to character one (no, he's not dead or in a coma!). Hence the flashback approach. It was all I could think of to give some concrete detail to character one's statement that she and character two had a relationship, the only way I could think of to show it. My worry is that even those one or two sentence-long flashbacks will throw the reader out of the story.
Did it work? Time will tell.