There was something in this week's episode that went understated, but it could be a stroke of genius if they use it the right way. While examining the organic residue that Peek-a-boo left behind, it was mentioned that the cells of the person she teleported took on properties of Peek-a-boo's own cells. Well, she teleported Barry.
One of Barry's more outlandish tricks in the comics was to vibrate his molecules so fast that he could become intangible and phase through solid matter. On the television series, Barry's encounter with Peek-a-boo may have just given him this added power, and he merely doesn't realize it yet. It would be an ingenious way to explain that iconic Flash ability.