If you enable "AirPlay" on Kodi it just works with Apple devices, in my experience. I'm not sure why there isn't something that easy for Android, but I suspect it's Google being evil and wanting you to buy one of their devices. Conceptually it's trivial with Pulseaudio to stream over the network. I ended up getting a bluetooth receiver for mine which allowed me to play from any phone (you do need to do a little bit of Pulseaudio config on the Kodi device, though).
Yes I tried via PulseAudio but it didn't work very well, and as it doesn't go through Kodi you can't see what's playing currently.
As for AirPlay, I only have android phones so I can't test it.
