Arrange the chicken strips in a single layer on a plate or baking sheet (this makes it easier to season and dredge them). Sprinkle evenly with 1/4 tsp. salt and 1/8 tsp. black pepper. Place the flour in a shallow bowl, and dredge the chicken in flour on both sides.
Place a large (12- to 14-inch) sauté pan over high heat for a couple of minutes. When hot, add the olive oil, swirl the pan to coat, and add the chicken strips in a single layer. Cook in batches if needed. Cook until slightly browned, about 1 minute. Turn the pieces or stir them so they brown evenly, about 1-1/2 minutes more.
Reduce the heat to medium-high. Push the chicken strips to the side of the pan as they continue to cook, and add the garlic. Cook just until fragrant, about 1 minute, but do not let it brown or it will taste bitter.
Add the tomatoes, season with 1/4 tsp. salt and 1/8 tsp. black pepper, and cook until they start to give off their juices, about 2 minutes.
Meanwhile, bring a medium (6- to 8-quart) pot of water to a boil. Salt it generously (it should taste like the sea). Stir in the pasta and cook according to the package directions. Drain (but don’t rinse, or you’ll rinse away starches that will help thicken the sauce) and return to the empty pot.
Add the spinach, oregano, remaining 1/2 tsp. salt, and remaining 1/4 tsp. black pepper to the pan with the tomatoes. Stir until the spinach has wilted, about 5 minutes. Add the wine to the pan, stirring to scrape up any browned bits, and cook over medium-high heat until reduced slightly and the chicken is cooked through, about 10 minutes.
Add the feta and olives to the pan, stirring well to incorporate. Remove the pan from the heat and stir in the butter, a tablespoon at a time, until the sauce has thickened slightly. (Careful! Your pan can’t be too hot or the butter and sauce will separate and look oily. If that happens, take the sauce off the heat and add more feta to help the sauce bind together.)
Stir the sauce into the cooked and drained pasta in the pot. Place over medium heat and simmer for 2 minutes to thicken the sauce and allow the pasta to absorb the flavors, stirring now and then.
Serve in individual bowls topped with Parmesan cheese.