Your body is getting rid of all the inflammation that was in your lungs due to smoking. You will cough up brown/gray mucous for a little while until it all clears out of your lungs. The time it takes can vary depending upon how much you smoked and for how long. Acid indigestion can cause a cough if you have the symptoms often and your throat is irritated but not usually phlegm. The acid will dissolve any mucous that is there anyway. Drink a lot of water to thin the secretions out, for singers there is a product called slippery elm and it comes in lozenges, can be found in a health food store, it is basically aspirin that comes from tree bark. Many opera singers use it to reduce inflammation in the vocal chords and preserve their voice.
Your body will take time to heal itself and consider the fact that smoking causes your cells in your lungs to change from epithelial cells (that can secrete mucous and have little hairs) to squamous cells that are basically scar tissue. If you have the squamous cells already it will be harder for the lungs to clear out the mucous and it will take longer. Good luck!