The third candidate in Tuesday's special election was Olive Branch security consultant Van Wicker.
The runoff is Nov. 27.
Republican Rep. Tommy Woods vacated the District 52 seat July 30 after serving 25 years in the district that covers parts of Marshall County and a sliver of DeSoto County.
Woods had suffered a mild stroke after last year's election but served during this spring's legislative session. He said he decided to resign on the advice of his physicians.
The winner will serve the final three years of a four-year term.
Special elections are nonpartisan, but Kinkade and Bryan say they're Republican.