How do I reuse part of a schematic in multiple projects in KiCad?
You can create hierarchical sheet and place there reusable part/circuit/module, create interface pins via hierarchical pin in sheet. But project resides in own directory you need copy schema file with hierarchical sheet. When you include in project you place hierarchical label to connect reusable part into project circuit. Such a sheet may be even reused more times in one project and multi-unit parts are allocated correctly. 

Note: Because referencing is maintained in file the file must be copied when used in second project. It's feature.