Season the chicken thighs with kosher salt and black pepper on both sides.
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 crispy, about 5-7 minutes. Flip and cook the other side for 3-4 minutes. Remove the chicken from the pot and set aside.
Reduce the heat to medium and add the diced onion to the pot. Sauté until softened, about 5 minutes.
Add the minced garlic, dried thyme, and crushed red pepper flakes. Cook for 1 minute until fragrant.
Pour in the chicken broth and diced tomatoes with their juice. Stir to combine and scrape up 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 drained 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 should reach 165°F).
Stir in the fresh lemon juice and adjust seasoning with salt and pepper to taste.
Serve the braised chicken with kale and white beans hot, spooning the broth over the top.