Start by placing the chicken breasts between two sheets of plastic wrap and gently pounding them to an even thickness with a mallet. This helps them cook through at the same rate without drying out at the edges. Season both sides lightly with salt and pepper before you begin the breading process.
Set up three shallow bowls: one with flour mixed with garlic powder and paprika, one with beaten eggs, and one with panko breadcrumbs. Dredge each chicken piece in flour, then egg, then press firmly into the panko so the coating clings well. This three-step breading is what gives the chicken its signature crunch.
Heat about half an inch of oil in a skillet over medium heat. Fry the chicken pieces for roughly 3–4 minutes per side, until deep golden brown and cooked through to 165°F internally. Transfer to a paper-towel-lined plate to drain excess oil before slicing.
While the chicken rests, whisk together mayonnaise, Dijon mustard, lemon juice, minced garlic, salt, and pepper in a small bowl. Taste and adjust the tang or seasoning as you like. This sauce ties the smoky, crunchy, and fresh elements of the wrap together in one bite.
Slice the rested chicken into thick strips. Lay a warm flatbread flat, spread a generous layer of the club sauce across the center, then add lettuce, tomato, avocado, chicken strips, and bacon in that order. Fold in the sides and roll tightly from the bottom up, just like you'd roll a burrito.
Cut the wrap in half on a diagonal so the colorful layers are visible, and serve immediately while the chicken is still warm and crispy. If you're packing it for later, wrap it tightly in foil to help it hold its shape.