The flagpole was targeted in the village of Sutton-on-Hull on the outskirts of Hull in the early hours of Saturday morning on July 31.
Officers said the pole was pulled down and snapped, causing damage to the flag which was there as a tribute to the village's men who died in WW1 and WW2.
Humberside Police have now released CCTV of two men they want to speak to in relation to the crime, which occurred at around 2.30am on Church Street.
A spokeswoman said: "We are appealing for anyone who might recognise the man in the CCTV images, or have seen a white young man with short light coloured hair, wearing a long sleeved top, shorts and dark trainers in the area at the time to contact us."
Anybody with information is asked to call 101 quoting reference number 16/78501/21, or alternatively, if you wish to remain anonymous, you can call Crimestoppers on 0800 555 111.