Salt the squirrel pieces well and then dust in flour.
Heat the olive oil in a large Dutch oven or other heavy, lidded pot over medium-high heat.
Brown the pieces of squirrel in batches. Make sure you don't overcrowd the pot. Move the browned pieces to a plate as they are cooked. Once the squirrels are browned, remove them all from the pot.
Add the onions to the pot. Saute the onion until the edges just begin to brown. Around 6-8 minutes.
Add the garlic. Cook another minute.
Add the tomato paste. Mix well and cook for 2 to 3 minutes. Stir often.
Pour in the white wine, vinegar, and water. Add the savory, red pepper flakes, and paprika. Add the tomatoes. Add the squirrel. Mix well and bring to a simmer.
Add salt to taste and cook gently until the squirrel falls off the bone. Around 90 minutes.
Take out the squirrel pieces and pull the meat off the bone. Return the meat to the pot.
Add the smoked sausage and the greens and cook until the greens are done.
Add salt, black pepper, chile, and vinegar to taste.