One of the things that has been on the to do list for a while with the Kaya theme is to add easy updating. It now is live and available in version 3.0.5.
You will still need to manually install version 3.0.5 using SFTP or using the Git Updater from Andy Fragen. But once you have version 3.0.5 or newer, future updates will arrive easily within WordPress.
Credit to slfrsn for the surprisingly small amount of code needed.