Checkerboard needs less help. A black-and-white top already supplies enough graphic punch that adding several retro references can make an everyday outfit look like a themed assignment. Keep the supporting cast quiet. Straight-leg jeans and simple sneakers give the pattern something ordinary to sit beside, so you get the throwback mood without dressing an entire decade.
Your jeans should relax. A straight leg falls without the close outline of skinny denim or the extra volume of a dramatic flare, leaving the top as the outfit's strongest visual statement. Try a familiar wash. Mid-blue denim softens the black-and-white contrast, while a hem that meets the shoe keeps the lower half from becoming another styling project. Skip the elaborate tuck. If the top feels boxy, a small front tuck can define your waist without making the whole outfit look carefully arranged for a photograph rather than worn outside.
Your sneakers should whisper. Plain canvas or understated leather works because it repeats the outfit's casual attitude without introducing another pattern, an oversized sole or a competing block of color. Accessories need restraint, too. A small bag and simple earrings are enough, especially when the checkerboard squares are large and occupy most of your torso. Leave matching checks alone. You can enjoy the retro reference without repeating it on your shoes, bag and sunglasses, which is where a playful top starts becoming a character. Would you actually wear that?