Pat the chicken thighs dry with a paper towel. Season generously on both sides with salt and pepper.
Heat the oil in your skillet over medium-high heat. Add the chicken in a single layer and sear for 4-5 minutes per side until golden brown. Transfer to a plate (they will not be cooked through yet).
Lower the heat to medium. Add the diced onion and cook, scraping up any browned bits, for 3-4 minutes until softened. Add the garlic and ginger and cook for 30 seconds until fragrant.
Pour in the coconut milk and chicken broth, stirring to scrape up any flavorful bits from the pan. Stir in the fish sauce and brown sugar.
Return the chicken to the pan, nestling it into the sauce. Bring to a gentle simmer, then reduce heat to low, cover, and cook for 10 minutes.
Remove the lid and increase heat to medium. Let the sauce simmer uncovered for 5-7 minutes until it reduces and thickens slightly, coating the back of a spoon.
Remove from heat and let rest 5 minutes. Shred the chicken with two forks right in the pan, stirring into the sauce. Divide rice among four bowls, top with chicken and sauce, and garnish with cilantro, red pepper flakes, and a squeeze of lime.