In a large pot of boiling salted water, cook the linguine according to package instructions until al dente. Drain and set aside, reserving 1 cup of pasta water.
In a large skillet, heat olive oil over medium heat. Season the diced chicken breasts with salt, pepper, and red pepper flakes. Add to the skillet and sauté until golden brown and fully cooked, about 6-8 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the cowboy butter and let it melt. Once melted, add the halved cherry tomatoes and sauté for 2-3 minutes until they start to soften.
Add the baby spinach to the skillet and cook until the spinach wilts, about 1 minute. Then, return the cooked chicken to the skillet.
Add the cooked linguine to the skillet, tossing everything together. If the dish appears dry, add reserved pasta water a little at a time until the desired consistency is reached.
Serve the linguine hot, garnished with fresh parsley and grated Parmesan cheese if desired.