To make the chicken, put flour in one shallow bowl, 2 eggs in another shallow bowl, and the panko breadcrumbs in a third shallow bowl. Season the panko breadcrumbs with salt and pepper. Scramble the eggs.
Take each breast and dredge it through first the flour, then the egg, then the breadcrumbs. Place the breaded chicken on a sheet pan and keep covered in the fridge for 20 minutes or up to 2 hours.
Make the sauce by whisking all ingredients (except the flour) into a medium saucepan. Add 1/2 cup water and bring to a light simmer. Once simmering, add the flour and whisk quickly to thicken. Taste the sauce and adjust as needed (needs to be sweeter? Add some white sugar. Needs to be more sour? Add more vinegar.)
Heat 1/4 cup veggie oil in a large fry pan over medium-high heat. Once hot, add the four chicken breasts. Reduce heat to medium. Cook the chicken for about 15 minutes, flipping once halfway through. Once chicken is cooked through, remove and place on a large cutting board. Cut the breasts into bite size pieces and set aside.
Clean out the large fry pan and add the remaining 1/4 cup veggie oil and heat over medium-high. Once hot, add all of the veggies and pineapple to the pan. Cook, stirring frequently, until the onions are a bit translucent and the peppers are softened. Add some of the sauce over the veggies and stir to coat with sauce.
Either in the same pan (if you have room) or a separate pan, add chicken and more sauce to coat.
Serve the chicken and veggies over white rice with more sauce on the side.