Burke was the lead partner in a Chicago law firm, Klafter and Burke, that specializes in representing clients in property tax appeals before the Cook County Assessor's Office, the Cook County Board of Review, and in the courts. The firm was successful in several "significant legal challenges" to Illinois real estate law. Burke's law firm's senior partner, Melvin Klafter, died on June 5, 1988 at age 73. The number of tax appeals Burke's firm filed for clients with the Board of Tax Appeals increased from 212 in 1982 to 1,876 in 1995. In 2002, Burke helped pass a city ordinance barring the city from contesting property tax appeals seeking a reduction in property assessment of under $1 million, which was most of Burke's cases. Between 2003 and 2013, Burke's firm won more than $18.1 million in property-tax refunds in Chicago.