The Chamfer tool is used to create a chamfer or flat bevel at the intersection of boolean operators.
It is not a general purpose chamfer tool, like blenders bevel tool is.
Chamfer can deal with tricky geometry overlaps and significantly reduce manual cleanup work as a result of these overlaps. It also as independent, per-side loop slide properties.
It is wise to run BooleanCleanup before using the Chamfer tool.
Select a loop of edges or vertices. It should be a cyclic selection, otherwise non-manifold geometry will be created.
cyclic edge loop at boolean intersection, a vert loop is fine as well