Pat the chicken thighs completely dry with a paper towel, then season both sides with kosher salt.
Place the chicken thighs skin-side down in a cold pan. Turn the heat to medium and cook undisturbed for 6-8 minutes, until the skin is deeply golden and the chicken releases easily from the pan. Flip and cook for a few more minutes, until the internal temperature reaches 160°F (it will climb to 165°F as it rests). Transfer the chicken to a wire rack set over a baking sheet so the skin stays crisp.
In the same pan, sear the lemon slices in the rendered chicken fat for about 1 minute per side, until lightly caramelized. Set aside on the wire rack with the chicken.
Reduce the heat to medium-low. Add the leeks with a pinch of salt and sauté for 3–4 minutes, until softened. Stir in the minced shallot along with a knob of butter and cook for 2 minutes more. Add the garlic and cook for 1 minute, just until fragrant.
Add in the uncooked rice and stir for 1 minute to lightly toast the grains.
Slowly pour in the chicken broth, stir to combine, and bring to a bubble. Reduce the heat to low, then nestle the cooked chicken back in skin-side up, keeping the skin above the liquid. Arrange the seared lemon slices over the chicken and rice.
Cover and let simmer for 12 minutes, or until the rice is almost perfectly tender. Turn off the heat and let the pan rest, covered, for 5 minutes.
Gently fluff the rice with a fork, then plate with the chicken thighs. Garnish with fresh dill and optional red pepper flakes.