hi - i don't use Keynote (yet) but since i know there are no problems inserting a SWF into PowerPoint, Keynote has to do the same.
do you know how to use XML with Flash ? i would have either a Dynamic text field that updates from the XML file. OR to be visually more stunning, you could have pre loaded into another folder that the XML references several images to represent the various possibilities of your vote. OR you could build an animated SWF like a pie chart, or a loading bar, or a bottle of champagne being filled, and having it dynamically load upon your vote ( variables/parameters). for example, if you have 200 members, voting for A or B , have 2 empty 'somethings" ( clock, pie, loading bar, champagne glass, etc) and when 10 people vote for A , then the A image loads/fills 5% ( 10 out of the possible 200 votes)
it depends on how comfortable you are with A) XML and/or B) ActionScript C) math !
whatever you choose to do, considering it is 'high profile' , TEST TEST TEST. do lots of dry runs, and it should be fine.
this is a cool, real -world problem, so
let us know how you choose to approach it,and if you need specific help in any of these areas - i am sure some of the experts will be glad to help you. i'll help if i can, too !