The User Scripts menu () provides a command to make a dialog into a stand-alone application. Your dialog being the active window, select User Scripts ▸ More Smile commands ▸ Dialogs ▸ Make a stand-alone application.

This command will make a new application in a new folder. You will be prompted for a location and name for the folder, and for a version number and a name for the application. The application is really a clone of Smile, bundled into a single file, with an initialization script which opens your dialog when the application is launched.
It remains your responsibility to quit the application (using the quit command) when the user closes the dialog. For instance install in your dialog's script a handler such as the following.

on delete theDialog
    continue delete theDialog
    quit
end delete

Further customization

When Make stand-alone application is done, the Console displays short instructions (and related lines of script) intended for performing a basic customization of your new application.

Still more options of customization are available. See all details in Customizing a stand-alone application.