Review the original item:
While flirting on the phone with the satellite dish salesman, Rose forgot
about the omelet cooking in the kitchen,
she was surprised when the stovetop fire filled the house with smoke.
You wanted to fix it this way:
While flirting on the phone with the satellite dish salesman, Rose forgot
about the omelet cooking in the kitchen,
consequently;
she was surprised when the stovetop fire filled the house with smoke.
A semicolon is an excellent method for fixing a comma splice. When you use this mark of punctuation, however, you must place it correctly in the sentence. You must put the semicolon at the spot where the two main clauses collide.
In the sentence above, the semicolon belongs before the transition consequently, not after it.
You might want to consult the rules for fixing comma splices and fused sentences.