Are you using Unity? I know I have not experienced this problem when running Opera-stable and Xubuntu 16.04. Maybe there's a bug in the GNOME shell, or within the Unity interface, that still needs to be worked out. I know sometimes these bugs can take months to get ironed out.
Although there's more initial customization that is needed when you first install Xubuntu, most people who begin using Xfce find that they enjoy the experience a lot. Ubuntu MATE is another very popular option. YouTube Xubuntu 16.04 and MATE 16.04 and take a peek at these two desktop environments. Install one, and then install Opera. I wouldn't be surprised if you find the flashing screens stops with Opera when running either Xubuntu or MATE.
I know, personally, that 64-bit Xubuntu and Opera-stable get along just fine on my Toshiba Satellite laptop.