I was having the same “authorization failed” problem and here is what worked for me. (Geez, what a f%$#&% tortuous path). In summary, you make the payment at www.avast.com and then you install from the Google Play Store.

From my Windows PC I went to the avast.com and select Store>Shop Now … scroll down to the Mobile section then select: >avast! SECURELINE>Android/Buy Now … (Only the 1 year subscription is offered, not the monthly plan)… Upon making payment (I used PayPal) select Download and it will direct you to the Google Play store… Meanwhile you get email notifications with the License Key… When you invoke the VPN ignore the “failed to initialize” message… At the top-right of the screen click on Subscribe (shopping cart icon), then select Have License… On the next screen go to the top-right corner and select “Use voucher”… where you then enter your License Key and that’s it.

The good news is that the fine-print states the VPN will work on other Android devices with the same email address. On my second device I uninstalled-&-reinstalled the VPN and it got activated without further hassle.