In the supplementary information for Org. Lett. 2005, 7 (19), 4297–4300, the following experimental method for the synthesis of 2-bromo-6-methylcyclohexa-2,5-diene-1,4-dione is given:
To a suspension containing 20.0 g (75.8 mmol) of 2,4-dibromo-6-methylphenol in 50 mL of 80% acetic acid in water and 25 mL of acetonitrile, was added 8.34 g of $\ce{CrO3}$ in 25 mL of water. The reaction mixture was heated to 60℃ for 1.5 h, cooled to room temperature, diluted with 400 mL of water and extracted with three 200 mL portions of chloroform.
I've summarised the reaction here:
How does this work, mechanistically? My first guess would be a nucleophilic substitution of $\ce{Br}$, followed by an oxidation by $\ce{CrO3}$; but I can't imagine there are many free hydroxide ions floating around in a solution of acetic acid.