KPM,
You seem to have the gist of it already. A Flotilla is simply a collection of ships which has a senior officer ( probably a captain if a destroyer flotilla - or even an admiral if capital ships are included)in charge of them and to whom all the commanding officers of the flotilla report. It doesn't mean that they all sail away together, they are more often engaged independently.
Small ships such as mineweepers, corvettes, diesel subs and the like have a depot ship, sometimes called a tender. This mother ship provides administration, pay, stores etc for the small ships. But the crews of the small ships would eat and sleep on their own vessel, and would operate independently from the mother ship for perhaps weeks at a time. An example is HMS Tamar in Hong Kong which is a shore base but which (when I was there anyway) looked after a flotilla of minesweepers and other small craft for the services I've described.
regards, Leofric ( Nine years before the mast...)
