That's one that requires research!
A strong candidate is Mount Saint Charles Academy Boys Hockey in the Div I for Rhode Island High School Ice Hockey.
Take a look here:
http://www.rihssports.com/
According to Wikipedia there has been 5 state championships
Safford high school.
Madison High School with 18
Washington High School of Sioux Falls, South Dakota has 39 state championships, they won 14 straight from 1952 to 1965
Seneca Valley high school with 12
New Trier
The Pine Bluff High School Zebras have 21 State Championships in Football.
no
East Grand Rapids Pioneers
Colleges can compete for conference championships not state
Mount Saint Charles Academy in Woonsocket, Rhode Island has won 26 High School State Championships in a row for boys ice hockey (1978–2003).
None in football one in baseball