Hey @Brandonrit! In your situation, you have two possibilities! With the Ring Video Doorbell 2 being battery operated, you do not need to hardwire it to your existing doorbell wires. You may mount the Doorbell 2 without attaching the wires and then, of course, setup the Chime/Chime Pro and link for notifications.
Your second option is to use the existing wires, bypass the existing chime kit and wire directly to your transformer following the instructions in this help center article.
Keep in mind, using the existing wires offers the benefit of a trickle charge to your Doorbell 2 battery. Remember to place the Chime strategically in your home for notification sounds to be heard best. I hope this helps!