In a shallow dish, add the flour, the salt, the thyme, the pepper, and the paprika and whisk to combine.
Light coat each side of the chicken breasts in the flour mixture.
Drain the sun-dried tomatoes, reserving 4 tablespoons of the oil.
In a large skillet over medium heat, heat 2 tablespoons of the sun-dried tomato oil until it is shimmering.
Add the chicken breasts to the hot oil and cook, turning them occasionally, until they are golden-brown on both sides, about 2-3 minutes per side.
Transfer the chicken breasts to a plate.
In the same skillet over medium heat, add the remaining sun-dried tomato oil.
Add the onions to the hot oil and cook, while stirring occasionally, until they soften and begin to caramelize, about 12 minutes. If the onions start becoming too dark too fast, add the water, a little at a time.
Add the sun-dried tomatoes and the garlic to the onion mixture and cook, while stirring, until warmed through, about 1 minute.
Add the white wine, the broth, and 1/2 of the lemon juice to the onion mixture and bring it to a simmer.
Simmer the onion mixture, while stirring frequently, until it has thickened into a sauce that coats the back of a spoon, about 10 minutes.
Reduce the heat to medium-low.
Add the chicken breasts to the skillet and cover the skillet.
Cook the chicken breasts in the sauce, undisturbed, until they reach an internal temperature of 165 degrees F, about 7-8 minutes.
Transfer the skillet from the heat.
Top the chicken breasts with the remaining lemon juice and the fresh herbs.
Serve with the capers.