When Barry was struck by lightning and went into a coma, Felicity constantly traveled to Central City to visit him at S.T.A.R. labs, where she met Wells, Cisco and Cailtin. However, in the Going Rogue episode of The Flash, Barry introduces her to Wells, Cisco, and Caitlin, saying, "This is Felicity Smoak, she works with the Arrow". Why would she need to be re-introduced when she's already spent a substantial amount of time with them from visiting Barry and from their interaction in season 2 of Arrow?
Out-of-universe, it was a way to prevent viewers who hadn't seen Arrow from being confused, while also getting in a nice plug for why they should go check it out.
In-universe, the man making the introductions was in a coma at the time. It's like introducing your girlfriend to your coworkers, when you didn't realize she used to work there too. Unless I'm forgetting a line, he simply didn't know they'd met and they were too polite to point out his mistake.
It's a bit late for this, but you've actually got the dialog in the scene a bit wrong. What actually happens is this:
Barry walks Felicity into STAR Labs and begins to show her all the cool toys. Caitlin and Cisco walk over...
Caitlin: It's so wonderful to see you again Felicity [emphasis mine], I'm just wondering how much of our operation she needs to know about.
Felicity: I'm really good at keeping secrets.
Barry: Yeah, Felicity works with the Arrow.
As you can see, Barry doesn't "introduce" Felicity to Cisco or Caitlin; it's clear they both already know her. What he does reveal is that she works with The Arrow... something neither of them would have known at that point. All they knew up until the was that Barry had gone to Starling City to work a case, that he had met Felicity there, and that she had come visit him while he was in his coma.