Slice the chicken breasts in half horizontally to make 8 thin cutlets.
Combine the honey, mustard, paprika, salt, pepper, lemon juice, and red pepper flakes, if using, in a large bowl. Remove ¼ cup of the mixture to a small bowl, stir in the mayonnaise, and refrigerate until ready to serve. Add the chicken to the remaining mixture and toss to coat. Cover and marinate in the refrigerator for 2 to 4 hours.
Cook the bacon in a large cast-iron skillet over medium heat, turning occasionally, until crisp, 5 to 6 minutes. Remove to a paper towel–lined plate and pour off all but 2 tablespoons of the bacon fat.
Increase the heat to medium-high. Working in 2 batches, cook the chicken in the remaining bacon fat until cooked through, 3 to 4 minutes per side. About 1 minute before the chicken is done, top each cutlet with 2 pieces of bacon and 3 tablespoons shredded cheddar and cover the skillet to melt, about 1 minute.
Spread the reserved honey mustard on the cut sides of each bun. Fill with the chicken (2 pieces per sandwich). Serve with pickles.