Place chicken onto a cutting board and pound lightly with a mallet to tenderize. Season all over with Kosher salt and freshly ground black pepper. Lightly coat in flour on all sides.
Melt 1 tablespoon of butter and heat 2 teaspoons of avocado oil in a large skillet over medium-high heat. Add chicken and sear until browned, 3-4 minutes on the first side and 1-2 minutes on the second side. Add another drizzle of oil, if needed. Turn off heat and transfer chicken to a plate. Wipe out any burnt bits from the pan with a paper towel.
In the same pan, heat 2 teaspoons of avocado oil over medium heat. Add shallots and garlic and cook, stirring occasionally, until golden, 1-2 minutes. Add white wine and cook until reduced by half. Add the chicken stock, Dijon, lemon juice, olives, olive juice, capers, bay leaf, thyme, and rosemary. Stir to combine and transfer the chicken back into the pan. Bring liquid to a simmer, then reduce heat to low and cover pan. Cook until the chicken is almost cooked through, 9-10 minutes.
Uncover the pan, turn the chicken completely in the sauce to coat, and raise the heat to medium. Cook for another 4-6 minutes, until the chicken is cooked through and the sauce is reduced and thickened. Remove from heat and stir in the chives and 1 tablespoon of butter. Taste and season with an extra squeeze of lemon, Kosher salt and freshly ground black pepper, if needed.
While the chicken cooks, heat a small dry pan over medium heat. Add the almonds and cook, stirring occasionally, until toasted and golden, about 3 minutes. Remove from heat and set aside.
Transfer chicken to a serving dish and pour sauce on top (alternatively, you can serve this directly in the pan). Garnish with toasted almonds, if using, and serve immediately.