How do you saute anchovies in a flavor base?
You can both chop or not chop the anchovies. 

I do not: I just crush them in the pan, and thus do not have to clean up anchovy oil from my cutting board.

I usually use anchovies like that in combination with garlic or onion, so the heat is never high enough to burn anything.  If your anchovies get burnt, lower the heat.