When I flush my toilet it makes a very loud rumbling noise that can be heard from other rooms, what could cause this?
Turns out the loud noise was caused by water rushing from other fixtures. The house had galvanized steel pipe as the main feed line (off the meter) which had become restricted, so when the toilet could not pull enough water from the main line it sucked it from other lines.
Replacing the galvanized pipe fixed the issue (as well as increased the pressure to the entire house).
From your comments, my guess is this is vibration of the drain line, and/or the vent stack, heard through the wall. I'll bet that one of those lines is not secured tightly, so you hear vibration in the wall to the kitchen. The vent stack may be touching the drywall in the kitchen, so you hear it "rumbling" in there, but not in the bathroom itself.
If you have access to this area in the basement, have someone stand down there with their hands tightly grasping the offending drain line/stack. The idea is to see if you can muffle the sound by dampening the vibration.
If this works, then the solution will depend on how well you can reduce those vibrations. Insulation might help, if you can stuff it up into the wall cavity next to the stack. Tie down the drain itself to nearby joists.
