The group was led by Vindicator and his wife Heather. James and Heather found Logan soon after he had escaped from Weapon X, though they were unaware of this. He appeared feral and they helped make him a civilized human again. Logan joined the team as Wolverine along with Puck, Snowbird, Shaman, Northstar, Aurora, and Sasquatch.
However, Wolverine left the team for some reason, presumably to join the X-Men. Eventually, Department H demanded that Wolverine come back to perform experiments on his adamantium skeleton, feeling it was rightfully theirs. Vindicator led the team to capture Logan, telling the others that Logan would be rejoining the team. Once captured, Vindicator gave Logan an ultimatum: either rejoin the team or have his indestructible skeleton repossessed. The other found out about this and fought to rescue Logan. When free, Logan warned them not to come after him again or he would take drastic action. Vindicator relented and let him leave.
This is currently the only version seen outside the comics. Their name is used in X2: X-Men United and a logo seen in X-Men Legends. Department H is seen in Hulk vs Wolverine and it is implied that Wolverine is a member of Alpha Flight.
This version is based primarily on the original incarnation from the early 1980's.
In the Comics
By the time the episode aired, James Hudson was called Guardian while Heather took the name Vindicator. He had previously used the name. In X-Men, she appears to have no powers. Her powers are similar to her husband's.
There is also a Beta Flight, Gamma Flight, and Omega Flight.