Wash and chop all vegetables into small, bite-sized pieces suitable for your dog's size. Cube the chicken breast.
In a large non-stick skillet or pot over medium heat, add the coconut oil. Add the cubed chicken and cook for 8-10 minutes, stirring occasionally, until fully cooked through and no longer pink inside.
While the chicken cooks, steam the carrots, green beans, and sweet potato in a steamer basket over boiling water for 10-12 minutes, or until tender. Add the peas in the last 2 minutes of steaming.
In a large mixing bowl, combine the cooked chicken, all steamed vegetables, and ground flaxseed. Mix thoroughly until evenly distributed. Let the mixture cool completely to room temperature before serving.