For Integrating GameCenter in your app you need to perform following steps:
1)Create a development provisioning profile at https://developer.apple.com/ in which GameCenter store technology is enabled.You can do this by referring the following link:
https://developer.apple.com/library/ios/#documentation/IDEs/Conceptual/AppDistributionGuide/ProvisioningStoreTechnologies/ProvisioningStoreTechnologies.html#//apple_ref/doc/uid/TP40012582-CH14-SW1
2)After creating provisioning profile,login into the https://itunesconnect.apple.com/WebObjects/iTunesConnect.woa using the same credential using which you create your profile.Click on "Manage your Apps" tab and then tap on the "Add New App" button.
3)Fill in the App name and select the bundle ID using which you create your provisiong profile and click on continue.
4)Click on Manage GameCenter button and add leaderboard and achievements information for your App.
5)For integrating game center API's in your app you can refer the docs at:
http://www.adobe.com/devnet-docs/gamingsdk/anedocs/com/adobe/ane/gameCenter/package-detail.html
6) After all this package your app using the provisioning profile created in step 1.
All the ANE's availaible with GamingSDK 1.1 can be used with both Flash builder as well as Flash Professional.
Please let me know if you required any further information.
Thanks,
Sakshi