First off, England was a monarchy, not a theocracy.
Second, the Pilgrims did not flee from England to America, but instead they left from Holland to America. They could practice their religion any way they wanted to in Holland, but they were concerned about their children becoming too Dutch, losing their English culture.
Finally, I'm sure the founders were more concerned about the Federal government intruding upon the states in the area of religion, as some states had official state churches at the time of our nations' founding, than any kind of concern about the new country becoming a theocracy.
The colonies had more than their share of "religious intolerance" during the colonial period. Some colonies were founded, because the faiths of their people were outlawed in other colonies.
England was also (and still officially is) a theocracy. After all, the ruler of England is head of England's official church. That said, England has traditionally been far more tolerant of different religions than either France or Spain, but less so than the low countries.