There is a reference to bicycle racing at "Kings Heath Enclosure" in The Bicycle 17th July 1946. The event was the Birmingham City Transport Sports which attracted a crowd of 15,000 people who saw Tommy Godwin take the 500 yards Scratch and 5 miles Scratch races.
There does not seem to be any other information on a cycle track at Kings Heath. There was a cinder greyhound stadium at Kings Heath from 1926, located on Alcester Road, which could possibly have been the venue.