Place a large skillet over medium-high heat, add bacon, and cook until browned and crisp. Remove to a plate and crumble or chop into small pieces. Leave all or most of the bacon fat in the pan.
While the bacon cooks, sprinkle the chicken breasts on both sides with garlic powder, about 1/2 teaspoon kosher salt, and a few cracks of pepper. Place flour on a shallow plate. Dredge each piece of chicken through it to coat on both sides, shaking gently to remove excess flour.
After removing the bacon, add chicken to the skillet and cook 3-4 minutes on each side, until just cooked through. Add a drizzle of olive oil if the pan starts to look dry. Remove chicken and set aside along with the bacon.
Add another drizzle of olive oil to the skillet, followed by the tomatoes. Cook for 2-3 minutes, until they begin to crinkle and soften.
Add broth and balsamic vinegar to the pan, scraping to release any browned bits. Bring sauce to a simmer and cook 1-2 minutes, until slightly reduced. Reduce heat to medium-low, then add cream and stir until the sauce is smooth.
Return chicken and bacon to the pan, then tuck spinach in around the chicken breasts. Simmer for 2-3 minutes more to thicken the sauce slightly, warm the chicken, and wilt the greens. Season with extra salt and pepper to taste, then serve and enjoy!