The writers left if open ended with a nod to the audience that he got away free. 'Breaking Bad': Creator Vince Gilligan explains series finale:
On the decision to spare Jesse and allow him to escape
“We found over the years that the way we can please the majority of the audience most of the time is to tune out as much extraneous factors as possible and please the eight of us in the writers room. If we can make ourselves happy day in and day out, we had a pretty good chance of making most viewers happy as well, and that’s what held us in good stead for six years. With that in mind, all [of us] in the writers room just loved Jesse (Aaron Paul) and we just figured he had gotten in way over his head. When you think of it, he didn’t really have a chance in the early days. Walt said, ‘You either help me cook meth and sell it, or else I’ll turn you in to the DEA.’ So this poor kid, based on a couple of really bad decisions he made early on, has been paying through the nose spiritually and physically and mentally and emotionally. In every which way, he’s just been paying the piper, and we just figured it felt right for him to get away. It would have been such a bummer for us, as the first fans of the show, for Jesse to have to pay with his life ultimately.”
On what happens to Jesse now
“We always felt like the viewers desired Jesse to get away. And it’s up to the individual viewer to decide what happens next for Jesse. Some people might think, ‘Well, he probably got two miles down the road before the cops nailed him.’ But I prefer to believe that he got away, and he’s got a long road to recovery ahead, in a sense of being held prisoner in a dungeon for the last six months and being beaten to within an inch of his life and watching Andrea be shot. All these terrible things he’s witnessed are going to scar him as well, but the romantic in [The Show Creator] wants to believe that he gets away with it and moves to Alaska and has a peaceful life communing with nature.”
That said, the DEA finds Walter dead in the lab. With the gun. His chem background, and all of Hank's info, pointed to him being the one running the lab. The DEA has everything to wrap the operation up, and will likely blame everything on Walt.