Cut each chicken thigh into 2 or 3 chunks. In a resealable plastic bag, combine flour, salt, and pepper. Add chicken, seal, and shake to coat.
Heat oil in a large pot over medium-high heat. Add chicken (discard excess flour) in a single layer and cook, turning once, until browned, 4 to 5 minutes total. Transfer to a plate.
Reduce heat to medium. Add garlic, capers, and red chile flakes and stir just until fragrant, about 30 seconds. Add tomatoes and simmer, scraping up browned bits from bottom of pan, until reduced by half, about 2 minutes. Add broth and chicken and return to a simmer. Lower heat slightly to maintain simmer, cover, and cook 10 minutes.
Add artichokes to pot and stir. Cover and cook about 8 minutes, until the stew has been heated through and reduced slightly. Stir in parsley and olives. Season with additional salt and pepper to taste. Serve hot.