Got a ring3 doorbell for Christmas. Took off my old doorbell button and replaced it with the (much larger) ring camera bell system. Existing bell is a simple mechanical battery operated loud bell. Whichever option I choose I can’t get the existing bell to ring. The helpline said it may be ‘incompatible’ …I don’t see how, when it’s a simple DC circuit. Seems like a ruse to get you to buy lots of add-on equipment. I’d not recommend anyone start on this expensive journey if you have an actual working doorbell already 
Ring doorbells do not work with battery powered doorbells of any kind… It works with hard wired powered systems only or with a Ring Chime as the chime inside the house.
Here’s a link for all the information on the doorbell.
Thanks for the info… if that is the case then I think that should be made loud and clear before you have to drill through your door frame to install the new Ring equipment…nowhere does it mention in the instructions not to drill your frame to install the device if your existing bell is battery powered. You’d think that would be key info? Secondly, it’s such a simple battery circuit, there is no logical reason that the ring doorbell couldn’t be compatible…it’s just a con to get you to buy more Ring gear. I’ll be warning off everyone I know!