64bit system. There is no sound. But if run out of Wine installed on my system, the sound is there. On my system, this would require a package i586-alsa-plugins-pulse.32bit.
I think analog lacking in your build?

Have you installed all packages listed in game's requirements? If you use Ubuntu, run this:

sudo apt-get install libc6:i386 libasound2:i386 libasound2-data:i386 libasound2-plugins:i386

I too had problem with sound, even though all libraries were present. The culprit was in path where libraries were looked for.
I edited support/gog_com.shlib and added ":$CURRENT_DIR/lib/i386-linux-gnu/alsa-lib/" to the LD_LIBRARY_PATH (see diff):

--- gog_com.shlib.orig 2014-07-29 16:17:43.000000000 +0200
+++ gog_com.shlib 2014-08-11 17:04:53.935846384 +0200
@@ -318,7 +318,7 @@


wine_export() {
- export LD_LIBRARY_PATH="$CURRENT_DIR/lib/:$CURRENT_DIR/lib/i386-linux-gnu"
+ export LD_LIBRARY_PATH="$CURRENT_DIR/lib/:$CURRENT_DIR/lib/i386-linux-gnu:$CURRENT_DIR/lib/i386-linux-gnu/alsa-lib/"
echo "LD_LIBRARY_PATH="$LD_LIBRARY_PATH
export WINEDLLPATH="$CURRENT_DIR/lib/wine"
echo "WINEDLLPATH="$WINEDLLPATH

Distribution does not use ubuntu. Accordingly, there are no packages that you specify.
Further more.
Bought Flatout 2, same problem, no sound. But, even worse, the game does not start on my native Wine, crushes it.

I think the experiment using Wine configured under a certain Linux distribution, it is very doubtful.

Alas, did not help :(
I added, as you pointed out, but the console displays the following

$ ./start.sh -w
Running FlatOut 2 windowed mode
WINEPREFIX=/mnt/wd1/tmp/FlatOut 2/prefix
GOG
LD_LIBRARY_PATH=/mnt/wd1/tmp/FlatOut 2/wine_standalone/lib/:/mnt/wd1/tmp/FlatOut 2/wine_standalone/lib/i386-linux-gnu

without the addition of lines
also

ALSA lib dlmisc.c:252:(snd1_dlobj_cache_get) Cannot open shared library /usr/lib/i386-linux-gnu/alsa-lib/libasound_module_pcm_pulse.so
ALSA lib dlmisc.c:252:(snd1_dlobj_cache_get) Cannot open shared library /usr/lib/i386-linux-gnu/alsa-lib/libasound_module_pcm_pulse.so

If I remove the line
export LD_LIBRARY_PATH="$CURRENT_DIR/lib/:$CURRENT_DIR/lib/i386-linux-gnu/"
it will still be displayed at startup

Since you're not using Ubuntu - what distro are you using?

Yeah, you're right. I was too fast to write.

There seems to be race between PulseAudio and Wine 1.6.2 which Flatout2 package uses.
I.e. when something is using PulseAudio (Firefox, Amarok, VLC...) and I start the game then there is no sound in game. When I make sure nothing is using PA, start the game, then I have a sound.

Take a look here, maybe it can help.

Thanks. It helped.