I am about to place 3/4" flooring in my house - the kitchen area has had 2 layers of vinyl. The first layer is glued to the 3/4 plywood, then 1/4" hardy backerboard has been placed on top of that with the 2nd layer of vinyl glued to the backerboard. The floor in the adjacent rooms are then 1/4" lower. Question - is it best to tear out the backerboard or should I just fan out felt paper to make a smooth transition from room to room. My first thougts are to tear out the backerboard but reading some posts I am not so sure now.

Any thougts?

I'd remove the 1/4" tile backer board and 2cd layer of vinyl on top of it. Then you'll be flush to the other areas. It's the way to go, IMO.

I would at the very least remove the top vinyl and 1/4" underlayment. The original vinyl depending on its age could contain asbestos, or it may be a full spread glue-down.

You could leave that layer and "feather" out from there if you choose to not disturb it.

It' best to take it all up, but not absolutely necessary.