Is the Award Fee Board Chairperson considered to be a voting member of the board?
While you do not work for the Air Force, a clue can be taken from the Air Force's Award Fee Guide
. Page 3 of the Guide identifies the Chairperson as a "member" of the Board. Then on page 16 of the Guide, the Board Recorder is identified as a "non-voting" member, but no such restriction is attached to the Board Chairperson on that page. In the larger context, I do not see any significant conflict in having the Chairperson vote, as the Fee-Determining Official makes the final determination of the fee amount.
Of course you should check with your organization's Contract Policy Office to see if there is local guidance specific to your activity.