prevent z-fighting between billboard particles? In an effect like blossoming flowers and many other particle effects the z order of individual particles doesn't really matter, so can I tell Blender to make them stop z-fighting and causing flickering and just assign order to each randomly, or some other solution?

Example blend: http://www.pasteall.org/blend/42258
If you would like to avoid Z-fighting you'll need to give your object at lest a small amount of difference in the location for every axis.

I would suggest to slightly increase the Velocity towards the Normal direction (e.g from 0 to 0.01) in order to not alter the overall look of the scene substantially, but at the same time, as each particle raise at different time, you'll have a variable distribution of particle location toward the camera.