Take a look at the original sentence again:
While flirting on the phone with the satellite dish salesman, Rose forgot
about the omelet cooking in the kitchen, she
did not expect the stovetop fire that filled the house with smoke.
You chose to fix it the correct way:
While flirting on the phone with the satellite dish salesman, Rose forgot
about the omelet cooking in the kitchen, so she
did not expect the stovetop fire that filled the house with smoke.
Rose forgot about the omelet cooking in the kitchen is a main clause. She did not expect the stovetop fire is the second main clause. An excellent way to join these two main clauses is to use a comma and a coordinating conjunction like so.