To use the Painter tool to add images to a collection in Lightroom, in the Library module, right-click on a regular collection (not a smart collection) and choose Set as Target Collection. Then, select the painter tool and choose Target Collection from the list of Paint options. While the painter tool is selected, clicking on an image in the grid to add it to the collection. You can also click – drag across multiple images to add them to the target collection.
The video below demonstrates how to set a target collection when creating collection, tapping the “B” key to add an image to the targeted collection as well as using the Painter tool to add images to a collection (2:15):