This might be obvious, but the Game runs on Vulkan, unless you manually switched to DX11.
If you have these problems with DX11, why did you switch off Vulkan? Or have you at all?
Older Radeon cards do not support Vulkan, so we have to run on DirectX 11. The game crashes if you try running it on Vulkan as there's no support.
I'm having the same issue on an AMD Radeon HD 6900. I've had the same issue with Mount & Blade 2 (if that's any help at all, I'm not sure if they fixed it). This was NOT an issue with Divinity: Original Sin 2. Sometimes tweaking some of the lighting options cause the lines to flicker more or less, and sometimes it generates weird particle effects, but mostly it's just a bunch of flickering mostly blue/green lines running horizontally through the screen. They DON'T seem to run over the UI overlay elements, only the main game scenes themselves. They run over a character's avatar 'cause I suppose it's generated and then inserted into the UI overlay.