Season the chicken thighs on both sides with kosher salt and black pepper.
Heat olive oil in a large heavy-bottomed pot or Dutch oven over medium-high heat.
Add the chicken thighs skin-side down and cook until the skin is golden brown and crisp, about 5-7 minutes. Flip and cook the other side for 3-4 minutes. Remove chicken from the pot and set aside.
Reduce heat to medium. Add diced onion to the pot and sauté until translucent, about 5 minutes.
Add minced garlic, dried thyme, and crushed red pepper flakes to the onions and cook for 1 minute until fragrant.
Pour in the chicken broth and diced tomatoes with their juices. Stir to combine and scrape any browned bits from the bottom of the pot.
Return the chicken thighs to the pot, nestling them into the liquid.
Cover the pot with a lid and reduce heat to low. Simmer gently for 25 minutes.
Remove the lid and add the cannellini beans and chopped kale to the pot. Stir gently to combine.
Cover and cook for an additional 10 minutes, until the kale is tender and the chicken is cooked through (internal temperature of 165°F).
Stir in fresh lemon juice and adjust seasoning with salt and pepper if needed.
Serve the braised chicken hot with kale and beans spooned over the top.