Mix flour, cumin, cinnamon, ginger, and salt together in a gallon-size resealable bag. Add chicken, seal bag, and shake to coat. Remove chicken and discard unused flour mixture.

Heat olive oil in a large pan or Dutch oven over medium heat. Cook and stir chicken in the hot oil, working in batches, until lightly browned, 3 to 4 minutes per side. Transfer chicken to a plate, reserving oil in the pan.

Saute onion and garlic in the same pan used for chicken until onion is translucent, about 10 minutes. Pour vinegar into the pan and bring to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon. Cook until most liquid is evaporated, 1 to 2 minutes.

Pour carrot juice into onion mixture and bring to a boil; cook until liquid is reduced by half, 10 to 15 minutes. Add dates, reduce heat, and simmer until liquid is 1/3 the amount as original amount, about 5 minutes. Reduce heat to low, add chicken, and simmer, gently stirring occasionally, until chicken is no longer pink in the center and carrot juice mixture is deep brown and thickened, 10 to 15 more minutes.