Season the chicken with salt and freshly ground black pepper then toss in the flour to coat.
Heat a large sauté pan until hot, add the oil and half the butter then fry the chicken pieces, skin side down, for 1-2 minutes until golden-brown. Turn the chicken and fry on the other side for another 1-2 minutes.
Meanwhile, heat a frying pan until hot, add the remaining butter and fry the bacon and button mushrooms until they are golden-brown. Add the shallots and caster sugar and fry for 2-3 minutes until golden and caramelised.
Add the wine and bring it to a simmer, stirring to deglaze the pan, then pour the bacon and mushroom mixture over the chicken. Add the stock, tomato purée and tarragon to the chicken and bring to the boil.
Reduce the heat to a simmer and cook for 30-40 minutes or until the chicken is cooked through and the liquid slightly reduced.
Meanwhile, for the mash, place the potatoes into a pan of salted water and bring to the boil. Reduce the heat and simmer for 12-15 minutes until the potatoes are tender.
Drain the potatoes and return them to the pan, then place the pan on the heat for one minute to steam off any excess moisture.
Mash the potatoes well, then add the butter and milk, beating to form a smooth mash. Season with salt and freshly ground black pepper.
When the chicken is cooked, add the tomatoes and flat leaf parsley, check the seasoning then simmer for a further two minutes before serving.
Serve two pieces of chicken per person with the sauce spooned over and a dollop of mash alongside.