I have COPD and need to clear phlegm from throat. What is the best method with which to do this?

Don't smoke. Quitting smoking is the best thing you can do to decrease sputum production. Using anti-inflammatory medications such as advair or symbicort (budesonide and formoterol) can also help in some cases as can treating any and all infections early.
Medicines can help. The phlegm that you have is probably a consequence of the copd. It is always good to get it out. Medications like Mucinex (guaifenesin) can help with this, as can nebulized medicines like albuterol/ipratroprium.