The offenders are reported to have entered a shop in Shakespeare Road, Gillingham, at around 8.45pm on 15 October 2020.
When inside the shop the three men had a verbal dispute with a member of staff and another shopper.
The customer, a man in his 30s, is then reported to have left the shop and was followed by the three men.
One of the offenders is alleged to have punched him in his face before they chased him and continued to assault him before they fled the scene.
Following the incident the victim received head, arm and leg injuries, and was treated at a local hospital before being discharged.
The suspects have been described as white and in their early 20s.
One offender was wearing a khaki green coat with a black fur hood, Adidas tracksuit bottoms, black trainers and a black baseball cap. A second suspect was wearing a grey body warmer and had brown hair.
Anyone with information is asked to call Kent Police on 01634 792209 quoting 46/185082/20.