I was playing Blitzcrank earlier today and his Rocket Grab says it stuns the target and pulls them towards you. I hit an Ezreal with it, and he used his E (not the Flash summoner spell) and was able to teleport out of my grab.

I've never been able to do that with Flash so is this a bug or am I missing something?

Its a timing thing. E does have a slight cast time, if he starts casting E before the grab hits him, even if the grab hits, he'll finish casting E and will teleport away.

He was already grabbed, a quarter of the way through the pull.

Yes, thats what happens, but if he already started casting E, when it finishes casting he'll go to where he teleported despite whether or not you've hit him with grab.

After he E's, is he stunned and your rocket grab is still attached to him briefly?

I'm not sure if this is intended, but it appears E can not be interrupted once he starts casting it, just like his ultimate.

Thanks for clearing that up. It seemed like a bug though, that's weird that it can work like that. Thanks again though gents!