Certainly he did, economic civil disobedience was many of the main forms of non-violent protest that King and many Civil Rights workers used before, during and after the Civil Rights Era. Economic Civil Disobedience can take many different forms, strikes, sabotage, workplace occupations, boycott, unionizing, all intended to disrupt the normal flow of money in a capitalist environment. Boycotts of white business districts were ruinous for local economies and were feared by many communities. An effective example of this is the Montgomery Bus Boycott in which the black community of Montgomery refused to use city buses or white operated taxi companies due to their segregation, this boycott drove many companies out of business and hurt the Montgomery economy so severely the local government desegregated rather than let the boycott continue. What the radio broadcast you heard was likely referring to was in Dr. King's last days, the reason he was in Memphis, and the economic civil disobedience he was advocating there.

Dr. King had come to Memphis to oversee and bolster the ongoing Memphis Sanitation Workers strike. Black Memphis Sanitation workers were protesting the terrible conditions they faced, they were consistently paid less, and faced a hostile, if not outright dangerous work environment. After the death of two sanitation workers in February of 1968, they began striking and protesting. Their main target was Memphis Mayor Henry Loeb, who had consistently refused to increase pay or ease working conditions for the black workers. On April 3rd, the day before Dr. King was killed, he gave a speech at a local Masonic Hall to thousands of the striking workers, urging them to continue striking and protesting against their unfair treatment. The day after, April 4th, 1968 he was assassinated.