You CAN make the SimpliSafe video doorbell work with most any chime

The Simplisafe "Chime Connector" might fix your problem, or not.  I needed more, and found that also adding a relay solved my problem.  Here's how...

The solution I found, in addition to using the "Chime Connectors" for both front and back doors, was to add a relay to the front door circuit - the other (back) works fine with only the Chime Connector, probably because of the way this particular electronic chime works.  It needs a diode installed across the front button, though they don't bother to mention which way it goes nor that it matters.  Therefore, obviously what this 16-volt chime needs is about 8 volts (it gets half-wave AC through the diode, which I think it "sees" as DC) to the front connection constantly, so that once the chime is started it can do the full Westminster chime (front) or the full ding-dong (rear).  Otherwise it only makes a sound while the button is being pressed and then stops.

But this diode messes up the SimpliSafe bell system on the front door, even with the chime connector.

I use the Chime Connector to trigger a relay, which triggers the chime itself.  More complication - my chime is 18 volts and I found no appropriate 18-volt AC relays available but lots of 24-volt ones, so I have 24 volts going to the relay.  Simplisafe doorbell camera works just fine with 24 volts.  I already have a 24-volt transformer installed because that's what my old chime used, so that was easy..

The Simplisafe video doorbell needs power which then comes through the relay coil (even with the Chime Connector powering the relay).  But that either operates the relay or buzzes it.  Gotta get power to the doorbell camera and not operate the relay till the button is pushed.  I had a few 10-ohm resistors on hand (because they were one solution suggested here for the electronic chime issue).  I figured out that one 10-ohm resistor across the relay coil wasn't enough, but 2 in series (that makes 20 ohms) is.  Relay sits there, the resistors and relay coil allowing enough power for the Simplisafe doorbell camera, and when the button is pressed the relay gets more current, it activates, and the relay triggers the chime.

If you do this, get larger resistors than the 1/2-watt ones recommended somewhere on this Forum.  They work normally but if he doorbell button is held "ON" for a moment rather than just pressed and released, the little resistors get hot and then begin to smoke.  I've got some 25-watt 20-ohm resistors coming to use in their place so this won't be an issue.  They're cheap.

Summary:

The camera needs constant power, which it gets through the chime, but that makes many chimes ring constantly.  The SImpliSafe Chime Connector may fix that or it may not.

Electronic chimes also need constant power to allow them to finish their ring after the doorbell button is released.  My particular chime needs a diode connected across the front button in order to send power to the FRONT connector, but that doesn't seem to work with the Simplisafe camera.  I actually installed the diode at the chime itself, on the 16-volt supply of the chime so it didn't interfere with the SImplisafe camera.

Despite the diode, my chime wouldn't work with the SS chime connector on the FRONT side and the camera didn't work that way either, so I trigger the FRONT with a relay, operated by the Simplisafe Chime Connector.  REAR works with just the Chime Connector and no relay.

It all works.  Good luck !!

PS -

PLEASE, SImplisafe, give us a schematic for the Chime Connector and the video doorbell (with specs - amp draw, etc.).  This could probably be done more simply, although what I did indeed works well.