Coughing up clear phlem with lots of brown spots?

Bronchitis?: Brown phlegm can be from dead tissue the body is eliminating as it fights infection (viral or bacterial) or can be old blood from inflamed airways or nasal bleeding that has drained down the back of throat. Could also be from pneumonia or even pulmonary TB. If no other symptoms & person is otherwise healthy nonsmoker, it's likely viral infection. See a physician if worried or worsening.

Could be blood: Sometimes old blood can look like brown flecks in sputum. Could also be residue from smoking if you are a smoker. If you are coughing real forcefully it is not uncommon to get a little blood in the phlegm, or if you have a very inflamed sinus infection or bronchial infection. I would recommend seeing your doctor to determine what the cause is and whether or not further studies are warranted.