Heat a dry skillet over medium heat. Toast chiles until fragrant, about 20 seconds. Transfer to a heat-proof container with a lid. Bring 5 cups of water to a boil and pour over chiles until just covered. Cover the container and set aside for 20 minutes.
Pour chicken broth into a slow cooker set on Low. Add goat meat, onion, garlic, salt, oregano, thyme, cumin, allspice, whole cloves, black pepper, and bay leaves.
Combine tomatoes, vinegar, and tequila in a blender and process until smooth. Add drained chiles and blend until as smooth as possible. Use a spoon to push the mixture through a small-holed strainer and add to the slow cooker; discard anything remaining in the strainer.
Cover the slow cooker and cook until meat is tender, 8 to 10 hours. Skim fat and strain juices before serving.