I could see it being one of two things.
One, it might be easier to have Espio be the focus of Rouge's affection, just because he's a side character. Usually, it seems like Rouge is either flirting with Shadow or Knuckles. Both of which are closer to being "main characters". Sega may just rather that Rouge flirt with a side-character, who can't headline their own game, rather than a a character who could, in theory, have enough name recognition to carry their own game.
Or two, it's just simple process of elimination. There's only three characters in the Chaotix (when Knuckles or Mighty and Ray aren't tagging along). Rouge can't flirt with Charmy because he's a child. And Vector canonically has a crush on Cream's mom, Vanilla, in most continuities, so she's probably not going to get too far with him. So, Espio's really the only one left for Rouge to flirt with. He's single, he's fun to mess with since he's pretty serious but not too serious like Shadow, and he has something in common with Rouge in that ninjas and thieves both sneak around. It kind of works.
It's probably Option #2. I doubt Sega has any problem with Rouge flirting with multiple characters, as long as it's kept pretty light and innocent. You never know with Sega, but I doubt it. Option #2 makes the most sense to me. Rouge and Espio are flirting because he's the only character here she could flirt with.
Plus, flirting in a detective noir story is just tradition! Rouge works pretty well as a femme fatale. And a femme fatale who doesn't flirt is no femme fatale at all! Sure, Rouge doesn't necessarily NEED to flirt with anyone for the story to work. But, it adds to the atmosphere and keeps the listeners guessing what her motives are.
Who knows if this "relationship" will continue on in the comics, or anywhere else? Espio doesn't get a lot of chances to show up, period, in the modern day. But, I don't think I'd mind it, myself. We'll see what happens.