I thought that was the Redtails of WW2?
They were indeed the RedTAILS, not hawks.
From their history page:
“The Allies called these airmen “Redtails” or “Redtail Angels,” because of the distinctive crimson paint applied on the vertical stabilizers of the unit’s aircraft.[7]”
Here: https://en.wikipedia.org/wiki/332d_Expeditionary_Operations_Group
It looks like the color scheme is more of a tribute to the Tuskegee Airmen than the actual name.