Can I install a rocket stove inside my house?
That will be up to the LAHJ - or Local Authority Having Jursidiction. Figure out who that is (if you need building permits, it's usually whoever issues and/or does inspections related to them) and ask.

Don't be overly shocked if the answer is no - I suspect most RMHs in dwellings are located in places with no or very minimal inspections/code enforcement, as the building code folks tend to be a bit conservative about fire and houses - not having people killed in house fires is a big part of why they exist. As such they can be very slow to accept non-traditional approaches to containing fires in houses. On the other hand, they may be able to suggest an approach that keeps them happy.