Unlike a display object's children, Starling and Feathers don't automatically dispose textures when a display object is disposed. You need to do that manually. The reason for this is that you may be using those textures in multiple places. If you have two Images, and they're both using the same texture, you don't want the texture to be disposed when you dispose one of the Images, but not the other one.
With that in mind, if you are creating a texture inside your screen, then it's your responsibility to override dispose() in your class and dispose the textures that you created. Don't forget to call super.dispose()!
Similarly, textures used by themes are disposed only when you call dispose() on the theme. If you were to have a different theme for different screens, for some reason (that would be out of the ordinary, but not completely implausible), then you'd want to dispose a screen's theme when the screen is disposed.