When I go to www.handheldcontact.com/ota, it will re-direct me to Google Play and display the Handheld Contact app for download.

After I select Install, the download doesn't do anything.

There are many reports (Android based) of users who are unable to download apps from Google Play.  This is on a individual device basis.  In order to correct this, simply shut down the phone, wait a moment and reboot it.  Then try again.  On an internal device, we needed to do this 3 times before Google Play picked up and downloaded Handheld Contact. 

Do not be concerned, just repeat the process and then eventually it will download as expected.