Many people use either propane burners or electric heat sticks (when not using their stove top)... Not heard of anyone using a kerosene burner for brewing...
You could use the BIAB method to start, unless you already have a cooler mash tun ready.
Can you get 6-7 gallons of water up to a boil on your stove? If so, you're set. Provided you have a large enough pot.
Another, more tricky, option would be to split the wort into two pots and boil it. You'll want to split the hops in half and add them to both pots at the same times.
Another option would be to make smaller batches... Personally, I'm not going down that route. I use a propane burner, 32qt kettle, plus a 5 gallon HLT, and my 70qt cooler mash tun... I just need a place to setup, brewing water and a water source to feed my IC to chill it on down.