I don't know Stage3D, and I'm talking in OpenGL language here, but the usual way to draw a background/skybox is to draw the background close up, not far, draw the background first, and either disable depth buffer writing while the background is being drawn (if it does not require depth buffering itself) or clear the depth buffer after the background is drawn and before the regular scene is.
Your flickering of planets may be due to lack of depth buffer resolution; if this is so, you must choose between
- drawing the objects closer to the camera,
- moving the camera frustum near plane farther out or far plane closer (this will increase depth buffer resolution across the entire scene), or
- rendering the scene multiple times at mutually exclusive depth ranges (this is called depth peeling).