Since the pattern on the chair is so bold I would stick to a lighter neural rug. You don't want to add anything too "busy" into the space. I think you're idea of an ombre fade would work well, in grey tones. Or a simple solid grey rug would also work!

The new chairs do seem to fight with what you already have- is there a specific reason that you chose them?

Something like this

Or

when choosing to add patterns, just take color pallet and proportion into consideration. If the chair pattern is medium size , rug should be 1/3 larger in print and and additional prints ( pillows or curtains) 1/3 smaller. I think you could easily use a black and white geometric shag rug with complementary throw pillows in colors and textures like 3rd pic.

Black and White Living Room · More Info

Emerald Gem · More Info