I don't have any AMD hardware, but these instructions should get you started:
In a terminal:
Code:
# see if the AMD driver loaded (should give you a driver date, which can be used to match with a catalyst version
$ dmesg | grep fglrx
# check if XBMCbuntu "sees" your HDMI audio device
$ aplay -l
# check to make sure that all digital outputs (PCM, S/PDIF, HDMI...) are unmuted (00 rather than (MM)
$ alsamixer
# check some basic analog output (CTRL+C quits)
$ speaker-test -D plug:hdmi
If the speaker test worked, then go into XBMC > Settings > System > Audio and choose "HDMI" if the PC is connected to a receiver. Choose "Analog" if the PC is connected directly to the TV. Then choose "hdmi (ALSA)" for the Audio Device (also for the Passthrough Audio Device if you picked "HDMI" at the top).
If it didn't work, post the output from the "aplay -l" command.
This page mentions that users with ATI cards may need to set the "radeon.audio=1" parameter either in GRUB or in the modprobe configuration.
EDIT: Good.
For desktop sound and menu sounds you will either need an ALSA configuration file or you can just configure pulse correctly. To configure pulse, try installing padevchooser. It should install the device chooser and a mixer (mixer should be all unmuted, device chooser should allow you to pick the HDMI output).