To install Adobe AIR on 32-bit Linux Mint, you can do the following:
Step 1: Use dpkg to enumerate adobe application
# dpkg -l | grep adobe
Step 2: Install Dependency for Adobe Flash
# apt-get install libnspr4-dev libnss3-dev libcurl3
Step 3: Download the Adobe Flash from http://www.adobe.com/
# dpkg -i install_flash_player_10_linux.deb
Step 4: Download the Adobe AIR from http://www.adobe.com/
# chmod 755 AdobeAIRInstaller.bin
# ./AdobeAIRInstaller.bin