In a large glass bowl, whisk together brown sugar BBQ grill seasoning, olive oil, apple cider vinegar, 1/2 c. Coca-Cola, red pepper flakes, and paprika.
Set aside 1/4 c. marinade.
Add chicken breasts to remaining marinade in glass bowl, stir to coat, and cover bowl with foil.
Place in the refrigerator to marinate for about 2 hours.
Meanwhile, add remaining Coca-Cola to a large saucepan.
Bring to a simmer over medium heat.
Simmer for about 1 hour, stirring occasionally, or until it thickens into a syrupy consistency, and reduces to about 1/2 cup. As the soda reduces, it will need more attention and stirring. It takes a while to significantly reduce, about 45 minutes, but then reduction happens quite quickly. Pay particular attention to the soda during the last 10-15 minutes of the reduction process.
Whisk in butter and salt.
Remove from heat, and carefully pour into a jelly jar or heat-proof glass jar.
Add reserved marinade to the Coca-Cola reduction, and stir to combine.
Remove chicken from refrigerator, and discard that marinade.
Grill chicken for 5-7 minutes on each side, basting with Coca-Cola mixture, or until internal temperature reads 165 degrees Fahrenheit.
Serve!