Heat 2 Tbsp olive oil in a skillet over medium-high heat. Add the sliced mushrooms and sauté until softened and lightly browned, about 6–8 minutes.
Transfer the cooked mushrooms to a food processor or meat grinder and pulse until finely minced; alternatively, finely chop by hand.
In a large bowl, combine the ground chicken, minced cooked mushrooms, grated onion, eggs, Panko breadcrumbs, salt, and pepper. Mix gently until just combined.
Scoop a heaping tablespoon of the mixture, place it into the flour, and dredge on both sides. Shape into oval patties (or round mini burgers for sliders), tapping off excess flour.
Heat 2–3 Tbsp oil in a nonstick skillet over medium heat. Add patties in a single layer without crowding. Cover and cook until golden, about 4 minutes on the first side.
Flip and cook the second side until golden and cooked through, about 2–3 minutes. Wipe the skillet with a paper towel between batches and add more oil as needed.
Remove cooked patties to a plate and serve warm.