When Spanish colonies in Latin America declared their independence in the 1800s, what did they use as a model for their governments?

Magna Carta

1 Bill of Rights

Mayflower Compact

U. S. Constitution

By the time Lat Am regions started going independent, Spain itself had experimented with constitutions that borrowed ideas from the constitutions of France. None of the examples you list along with your question served as models ... there were plenty of other well-known constitutions to draw ideas from (France and Spain had had several by then). If credit is to be given as to the source content of such constitutions, it would be to the ideas of Locke and Descartes.