wget http://airdownload.adobe.com/air/lin/download/2.6/AdobeAIRInstaller.bin
chmod +x ./AdobeAIRInstaller.bin
sudo apt-get install libxt6:i386 libnspr4-0d:i386 libgtk2.0-0:i386 libstdc++6:i386 libnss3-1d:i386 lib32nss-mdns libxml2:i386 libxslt1.1:i386 libcanberra-gtk-module:i386 gtk2-engines-murrine:i386
sudo dpkg-deb -R libgnome-keyring0_3.8.0-2_i386.deb gnome-keyring
sudo cp gnome-keyring/usr/lib/i386-linux-gnu/libgnome-keyring.so.0.2.0 /usr/lib/i386-linux-gnu/
sudo ln -s /usr/lib/i386-linux-gnu/libgnome-keyring.so.0.2.0 /usr/lib/i386-linux-gnu/libgnome-keyring.so.0
Create symlinks to gnome-keyring so Adobe Air could see it:
sudo ln -s /usr/lib/i386-linux-gnu/libgnome-keyring.so.0 /usr/lib/libgnome-keyring.so.0
sudo ln -s /usr/lib/i386-linux-gnu/libgnome-keyring.so.0.2.0 /usr/lib/libgnome-keyring.so.0.2.0
sudo apt-get install libgtk2.0-0:i386
./AdobeAIRInstaller.bin