Why did the Puritans promptly establish their own church and persecute dissenters? After all, they fled those same things in England.The Puritans...

The reason for this is that the Puritans did not believe
in religious tolerance.  They were fleeing persecution, it is true, but that does not
mean that they thought all religions should be free to worship in peace.  Instead, what
they wanted was for their religion to dominate.

The
Puritans believed that God would punish any society that did not enforce the proper
beliefs and actions.  They felt, therefore, that the presence of other religions (or of
dissenters from their own religion) in their society would bring God's wrath down upon
them.  For this reason, they did not tolerate dissent.