The Quick Search Shortcut is the best way to search for a canned response.
While using the app, press Alt+C (this is customizable if you want to change it later on) at any time to select the search bar and start searching a canned response.
If you are using the Desktop App, you can use this shortcut anywhere, even when typedesk is hidden, to start searching a canned response and automatically paste it where you are typing.