I used to be a "Gym Leader" in a competitive battling league/forum and I was Flying. But the rules there were that only 4 (or more) of the 6 Pokes had to be part Flying. In the short time that the league existed, I was 8 for 8 in defeating challengers (who could bring any Pokes they wanted to battle me).
So I would be an Elite 4 member, similar to Lance in the games where not all Pokemon followed one type, but Flying would be a common theme like Dragon was for Lance.
So Swampert (lead) and Heatran are the non-flyings, which play very well for people who think they can run in with a few Ice/Electric pokes. Swampert is immune to Electric, so is a nice switch in from Gyarados. Heatran resists Ice by 1/4 and would be a great switch in from Skarmory predicting a fire attack.
But Honchcrow is the signature Poke, his name is Lenny, and he is a boss.