Flash starts being friendly towards Peter after Uncle Ben dies, remember when Flash was trying to console Peter? Flash may have been a jerk but in the end he knew Peter and chose to toss aside his problems with Pete, he understood what Peter was going through. How is that unrealistic? That's maturing! Peter, on the other hand, becomes more confident in himself when he becomes Spider-Man. His relationship with Gwen also helps him come out of his shell and starts to be a lot friendlier to others, even Flash. They're both smart kids and you could tell Gwen liked Peter before he was Spider-Man, so when he revealed his identity as Spider-Man their hormones obviously go flying.
Also why should Spidey show a grown man who happens to be a car thief humility or respect? Spidey's banter has always had the purpose of driving his enemies nuts so he can take em out easily. It was also his first night going out as Spider-Man and at the time he had a vendetta and was trying to catch Uncle Ben's killer (which he then realised was wrong), so there was always going to be a hint of aggressiveness around him.