The date of the start of the Vega Campaign differs depending on source... In the original WC1 and its manual it is set around 2654.110. According to the Pilgrim Truth its some point after .163 after Paladin's court martial and his return to the Claw. The Wing Commander I&II Ultimate Strategy Guide may have it as late as August/September 2654, but it is not specific. This wiki follows the novel timeline as to Claw's main entrance into the campaign, but considers the 2654.110 to be official start of the campaign.
The end of the campaign is generally said to be around 2654.325.
Note: There is another alternate timeline for the campaign related to LaFong see Bible timeline but this one is generally ignored as it was not officially published, it places the events of the campaign as early as .084 (which overlaps too much with the Wing Comander movie trilogy)