Put the flour in a shallow dish or plate and season lightly with salt and pepper. Heat the olive oil and butter in a large frypan over medium-high heat. Season the chicken breasts with salt and pepper and coat each with the flour.
Cook the chicken in the hot oil and butter until golden, about 3 minutes. Turn over and brown on the other side, 3 additional minutes. Remove chicken from frypan and keep warm in alfoil.
Reduce heat to medium. Stir the red onion into the oil and butter left in the frypan. Cook until softened, 2 to 3 minutes.
Pour the chicken stock into the pan, and simmer while scraping the browned bits of food off the bottom of the pan with a wooden spoon. Pour in the wine and bring back to a simmer. Cook the sauce until reduced by half, about 3 minutes.
Return chicken to the pan along with any juices that have accumulated. Simmer chicken in the sauce until it is cooked through and no longer pink in the centre, 3 to 4 minutes. Transfer chicken to a warm plates.
Whisk the mustard and sour cream into the sauce in the frypan; stir in the tarragon. Spoon sauce over chicken to serve.