In a deep-fryer or heavy-bottomed pot, heat enough canola oil to come halfway up the sides of the pot, to 375 degrees F. Preheat the oven to 375 degrees F.
Put the garlic, vinegar, mustard, horseradish and rosemary into a food processor. Pulse the ingredients until smooth. Slowly add the olive oil to emulsify and season with salt and pepper. Put the chicken in a large resealable bag. Pour the marinade into the bag and mix it into the chicken until well coated. Close the bag and refrigerate for 2 to 4 hours and up to overnight.
Put the flour in a shallow dish. Remove the chicken from the marinade. Dredge each piece of chicken in the flour, shaking off any excess. Working in batches, fry the chicken until golden brown, about 7 to 8 minutes. Remove the drumsticks from the fryer and arrange them on a sheet tray. Put them in the oven until cooked through, about 6 to 8 minutes. Remove the chicken from the oven and arrange them on a platter for serving.