JFK was a proponent of interventionist foreign policy and neoliberal-ish economics just like every US president after him. The US establishment had no reason to kill him. He was one of them through and through.
The Kennedy speech came shortly after the failed "bay of pigs" operation - on April 27. There might have been some tensions between the various branches of government on that occasion, so it can have more than one interpretation. Here is the full text:
