ADEN, Yemen—At checkpoints across this war-racked city in southern Yemen, local fighters wearing flip-flops and carrying Kalashnikov rifles fly the flag of the United Arab Emirates.

Some of the men fighting the pro-Iranian Houthi militia have taken to wearing soccer jerseys with the Emirates Airline logo, instead of uniforms. Civilians often drape U.A.E. flags over the hoods of their cars as they navigate past bombed-out high-rises and the charred hulks of tanks that were part of the Houthi rebel force that recently occupied...