My logs:
The I2S line looks good.
This lines of your log are a potential problem:
Code
Jun 22 13:11:51 KODI-Nappali pulseaudio[265]: W: [pulseaudio] main.c: Running in system mode, but --disallow-module-loading not set.
Jun 22 13:11:51 KODI-Nappali pulseaudio[265]: W: [pulseaudio] main.c: Home directory of user 'root' is not '/var/run/pulse', ignoring.
Jun 22 13:11:51 KODI-Nappali pulseaudio[265]: W: [pulseaudio] caps.c: Normally all extra capabilities would be dropped now, but that's impossible because PulseAudio was built without capabilities support.
Jun 22 13:11:51 KODI-Nappali pulseaudio[265]: W: [pulseaudio] main.c: OK, so you are running PA in system mode. Please make sure that you actually do want to do that.
Jun 22 13:11:51 KODI-Nappali pulseaudio[265]: W: [pulseaudio] main.c: Please read http://www.freedesktop.org/wiki/Software/PulseAudio/Documentation/User/WhatIsWrongWithSystemWide/ for an explanation why system mode is usually a bad idea.
Jun 22 13:11:51 KODI-Nappali pulseaudio[265]: W: [pulseaudio] authkey.c: Failed to open cookie file '/var/run/pulse/.config/pulse/cookie': No such file or directory
Jun 22 13:11:51 KODI-Nappali pulseaudio[265]: W: [pulseaudio] authkey.c: Failed to load authentication key '/var/run/pulse/.config/pulse/cookie': No such file or directory
Jun 22 13:11:51 KODI-Nappali pulseaudio[265]: W: [pulseaudio] authkey.c: Failed to open cookie file '/var/run/pulse/.pulse-cookie': No such file or directory
Jun 22 13:11:51 KODI-Nappali pulseaudio[265]: W: [pulseaudio] authkey.c: Failed to load authentication key '/var/run/pulse/.pulse-cookie': No such file or directory
I don't have those pulseaudio warnings in my kodi.log, but I don't have a Hifiberry shield.
Maybe user HiassofT can have a look at his log to verify whether the warnings are critical or not.