Pat the chicken breasts dry with paper towels—this ensures better browning. In a shallow bowl, combine the flour, salt, and pepper. Coat each chicken breast evenly on both sides with the flour mixture, shaking off any excess. Set aside on a plate. Mince the ginger and garlic, and trim and slice the sugar snap peas diagonally. Having everything prepped before you start cooking ensures the dish comes together smoothly without interruptions.
Heat the olive oil in a large skillet over medium-high heat until shimmering, about 2 minutes. Working in batches if needed to avoid crowding, place the flour-coated chicken breasts in the pan and sear for 6-7 minutes on the first side until golden brown. Flip and cook the other side for another 6-7 minutes until the internal temperature reaches 165°F. Transfer the cooked chicken to a clean plate and set aside.
In the same skillet with the rendered chicken drippings, add the minced ginger, garlic, and red pepper flakes over medium heat. Stir constantly for about 1-2 minutes until fragrant and the mixture begins to caramelize slightly—this develops deep, complex flavors. Add the soy sauce, brown sugar, vinegar, fish sauce, and sesame oil, stirring to combine. I like to taste the sauce at this point and adjust the balance; if it's too acidic, I add a touch more sugar, and if it needs more depth, a splash more soy sauce works perfectly.
Bring the sauce to a gentle boil, then reduce the heat to medium-low and simmer for 5-7 minutes, stirring occasionally, until the sauce reduces by about one-third and thickens slightly. The sauce should coat the back of a spoon. Return the cooked chicken to the skillet, nestling it into the sauce, and simmer for another 2-3 minutes to allow the chicken to absorb some of the flavors and warm through.
Add the sliced sugar snap peas to the skillet and toss gently to coat them in the sauce. Cook for 1-2 minutes just until the peas are heated through but still retain their crisp-tender texture. Transfer the chicken to serving plates, spoon the sauce and vegetables over the top, and garnish with fresh cilantro.