Heat a 10-12” nonstick skillet over medium-high heat and add the olive oil. Sautee the onions for a few minutes until translucent. Add in the garlic, salt, pepper, oregano, thyme, basil, and red pepper flakes and cook for another minute or two until the garlic is fragrant.
Crush the tomatoes and add to the skillet along with all of the juice from the can. Add in the vinegar and stir to combine with the onion, garlic, and seasoning mixture.
IF USING A SLOW COOKER: pour the sauce mixture into the slow cooker and nestle the chicken breasts so they are submerged in the sauce. Cook on low for 7-8 hours. Remove the chicken and shred on a separate platter. Use an immersion blender to purée the sauce mixture until smooth. Return the shredded chicken to the sauce and stir well to combine.
IF USING A THERMAL COOKER: pour the sauce mixture into the inner thermos pot and nestle the chicken breasts so they are submerged in the sauce. Put the lid on and bring to a rapid boil for 5 minutes then reduce to simmer for an additional 5 minutes. Remove from heat and transfer to the outer thermos to cook for 7-8 hours. Be sure you have enough contents in your inner pot to be 75-80% full for proper cooking. After cooking, remove the chicken and shred on a separate platter. Use an immersion blender to purée the sauce mixture until smooth. Return the shredded chicken to the sauce and stir well to combine.