Well, the first thing you should probably do is grab a heart scale and get Chesnaught to relearn hammer arm. That should let him lead off against the Cinccino, tank whatever it wants to do and kill it in one hit. Girafarig shouldn't be a problem, just kill it with Zoroark. The big threats to your team are his Porygon-Z, Swellow, Staraptor, and Clefable. Keep Gyarados away from Porygon-Z as I think it knows discharge. He'll be your best bet at killing the birds though, even then he's not the best answer to them. Use Fake out on Hariyama to rack up more status damage on the Swellow if one of your guys goes down. Noivern can probably revenge kill the Staraptor due to it's poor special defense and lower speed. I'm pretty sure Porygon-Z knows psychic as well but if Hariyama can tank one then it can probably kill it with Fake Out and Force Palm. Don't quote me on that though. The Clefable's going to be the real threat, I'm assuming it has moonblast, and that's super effective against 4 of your pokemon. Also you don't have one super effective attack to hit it back with.
If you find you can't beat him with this team then my best advice would be to grab something that can reliably deal with the birds alongside an Escavalier. Seriously, my Escavalier absolutely wrecked him with iron head, swords dance and all that bulk.