Start with the pattern
A radiator that is cold at the top may have trapped air. One that is cold in places at the bottom may have poor circulation or debris. If the radiators furthest from the boiler stay cool, the system may need balancing.
A stuck valve can also leave one radiator cold while the rest of the system works normally.
Balancing and flushing are different jobs
Balancing adjusts the flow through each radiator so heat is shared around the system. Flushing cleans contamination from the water and pipework. Doing one does not automatically solve a problem caused by the other.
I test the system before recommending a flush. If a valve, pump or control is the real fault, cleaning the water will not repair it.
Protecting the system afterwards
After work on the heating system, it needs filling, treating and checking properly. A magnetic filter can help collect circulating debris, but it does not replace correct diagnosis or maintenance.