Thank you for posting your request on History Hub.
The National Archives has a number of resources relating to the topic of African Americans and military service. The following is a research guide that has compiled a list of records of Military Agencies relating to African Americans from World War 1 to the Korean War.: https://www.archives.gov/files/publications/ref-info-papers/105/index.pdf
Additionally the staff of the National Archives have created a Webpage to assist with the locating of records documenting the Black experience: https://www.archives.gov/research/african-americans?_ga=2.125233418.120043236.1620046405-1999831461.1604948817
You may want to look at Unit records for the specific units that were stations at Burtonwood Airbase during World War II. Most of the unit records for the United States Army Air Forces are held at the National Archives at College Park, MD and you can contact their reference staff at email@example.com.
We hope that this information was helpful to you and good luck with your research.
There is a book titled: "When Jim Crow Met John Bull, American Soldiers in World War II Britain, by Graham Smith.
There is no mention of the US Base you mentioned but the bibliography has a lot of information.
I hope this helps.