We had to remove King Palms that were getting into drainage lines and now have the problem of stumps and roots. Is there an easy way to get rid of both (i. e. poisoning and burning)?
You can kill the stumps by drilling holes into the stump and pouring Round-up into the holes. Repeat every few weeks to make sure it is dead. This will at least stop it from growing further into the drain lines.
I personally like to use a sawzall when removing stumps. You can plunge the disposable blade into the soil around the stump and cut through any roots. Then just lift the main part of the stump out.
My car and driveway are covered in little sap spots from my king palm.
It sounds like your king palm might be afflicted with scale. Please read the following article to verify this diagnosis and administer the prescribed treatment for it, if it is present: