Yes applying Listerine to your area where the Jock Itch is can help kill off the bacteria causing the Jock Itch.
Listerine contains Alcohol which is antibacterial, Anti Fungal and Antiseptic so it can kill off the bacteria and cure Jock Itch.
Apply the Listerine up to 3 times per day and do not wash it off as the Listerine will evaporate itself from your skin.
You can also cure Jock Itch using Apple Cider Vinegar and just apply it like you would the Listerine.