I understand the Tube is the best way to get from Heathrow to Kings Cross. Does this journey have escalators and lifts all the way? I am unable to carry my cases.
In this guide you will see that all the Heathrow stations, as well as King’s Cross St. Pancras, are marked with Lift access between street and platform, and additionally all have the Platforms with designated level access boarding point indication, which means that at certain points along the train there will be level access all the way onto the train (so you won't have to step up or down).
You will be able to wheel your cases the whole way.
Just looked it up on Transport for London's Journey Planner for Heathrow to King's Cross with Full step free access and TfL recommends taking the Heathrow Express to Paddington and then the Circle Line to King's Cross. Without Full step free access TfL recommends taking the tube straight to King's Cross via the Piccadilly line.