There should be nothing blocking you from installing it. Some players have been reporting issues and we are looking into them. However you should be able to download the installer from here and if for some reason that does not work I would go ahead and clear the Blizzard app cache by following the steps here and give it another shot after restarting your computer.
Bill Warnecke
Also the free trial requires PS Plus, do you have this?
Bill Warnecke
The trial is working as expected on PlayStation 4. I'd recommend trying to restart your console to see if it appears if you're not seeing it.
Bill Warnecke
Hey there, we're working on a fix for people who aren't seeing the free weekend show up on PC.
More details are available in our tech support forums. Here's a workaround.