Arrange chicken breasts in a single layer on a work surface and cover with plastic wrap. Using a heavy skillet or a rolling pin, pound them until flattened to about 1/2 inch thick.
In a shallow dish, combine the flour, salt and pepper. Dredge both sides of each breast in the seasoned flour.
In a large nonstick skillet over medium-high, heat the oil and butter. Add the chicken breasts and cook until they are well browned on both sides and no longer pink at the center, about 4 minutes per side. Transfer them to a plate and cover with foil to keep warm. Do not clean the skillet.
While the chicken breasts are cooking, drain the juice from the pineapple into a measuring cup. Add enough orange juice to total 3/4 cup. Stir in the cornstarch, then set aside.
Return the skillet to the stove over medium-low. Add the drained pineapple and brown sugar. Cook, stirring constantly, until the pineapple begins to brown, 3 to 4 minutes. Add the chilies and garlic and stir until the garlic is beginning to color, 1 to 2 minutes.
Stir in the reserved juice. Bring the sauce to a simmer and cook until thickened and reduced slightly, 4 to 5 minutes. Stir in the cilantro, then serve, spooned over the chicken breasts.