In Breaking Bad Final Season, when Walt meets Jesse with Saul and asks Jesse to leave town, Jesse breaks into tears and says to Walt that why doesn't he tell him straight away what he wants or he will kill him as he killed Mike.
How did Jesse know that Mike is dead and that Walt killed him?
Jesse has seen first hand how ruthless Walt can be to anyone he perceives as a danger. Mike and Walt had never been on good terms but Mike had always cooperated with Walt's schemes after some persuasion. The only glaring exception was handing over the names of Mike's associates residing in prison. Jesse knew how paranoid Walt felt about leaving those men alive, and how protective Mike was of them. So when Mike's sudden disappearance coincides with the synchronized executions of Mike's men, Jesse knew something was very fishy. Mike would never abandon his men that way. The only way Walt would've been able to safely go through with his plan was for Mike to be out of the way. Jesse is smart enough to add two and two together and deduce that Walt had killed Mike as well.
He doesn't have any definitive evidence so he can't be 100% sure.
However he knows what Walt is capable of and has seen what can happen to people who put Walt in danger. Either in physical danger (Gus) or in danger of being caught (Prison inmates).
I think it's fair to say Jesse makes the presumption that Walt kills Mike based on what has happened before rather then definitive evidence.
Jesse knew that by looking at how comfortable Walter was in his position. He knew Walter well enough to understand what could signify this comfort, the fact that Mike is no longer a threat.
