If you're using an Intel processor, try running your display through the integrated HDMI output on your board. Run a game on its integrated graphics. If the textures flicker, it's something else in your system (RAM, CPU, board). If they don't, it might be your card.
Run some benchmarks (I'd try Valley) on your "faulty" card and see what happens. Monitor your temperatures, clock speeds, and power states during these. I assume you know what are considered safe and unsafe operating temps, so go through that evaluation process. Check for big & abrupt changes in clock speeds and power consumption. These could point towards a faulty PCIE lane or PSU, respectively or combined.
If none of those yield any obvious conclusions, try the...