removing OSB Underlay??
Unfortunately, there's no "easy" way to remove glued vinyl and flooring. If you want the floor levels to be flush and even from one room to another, now is the time to cut out the kitchen flooring level above the subflooring.
Use a circular saw with an old blade (you WILL hit nails or screws) adjusted to the depth of the flooring above the subfloor, and safety glasses. Cut it out in no more than 2' squares or so for easier removal, and pry the sections to be removed up with a flatbar, crowbar, clawhammer, etc. to remove it.
Depending upon when and how your home was built, you may have 3/4" subflooring + 5/8" flooring + the 1/4" OSB (probably used for leveling) and the vinyl.
You'll have to cut into it to see what you actually have, then remove what is necessary to get the floors to come out level from room to room
A word of caution about installing hardwood, tile, etc. in a kitchen. If you decide to raise the level of the kitchen flooring, you may trap the dishwasher in the cabinet base. Raise the cabinet base and dishwasher to the new floor level with plywood and shims. (I always use pressure-treated plywood anywhere there's going to eventually be a water leak, but that's your call.)