The orange-stripped flags, which feature the slogan ‘Following the Tigers to Wembley’, will be available from MKM branches in Stoneferry, Hull, Springfield Way, Anlaby and Swinemoor Lane, Beverley, all week from Monday 12 May.
They will be given out on a first-come-first-served basis and fans are warned to get theirs early as demand is likely to be high.
David Kilburn, chief executive of MKM Building Supplies, said the flags were the company’s way of showing support for Hull City in the run up to the historical battle.
He said: "The Tigers have achieved so much over this last year, more than anyone could have dreamt of at the start of the season, and to be playing in the FA Cup final against Arsenal is pinnacle of that."
"We sponsor the south stand at the KC Stadium and have done for some time, but we wanted to go further in the running to Wembley and publicly demonstrate our support for the Tigers across the city and wider region."
"That’s why we decided to give away the flags. We have thousands of them available and hopefully, when fans display them on their cars it will help add to the atmosphere of excitement and anticipation which is already building up."
Mr Kilburn added that although Hull was certainly the underdog, he thought a shock victory was not beyond their grasp.
"After everything the club has achieved this year anything is possible so I will be keeping my fingers crossed."