Skype is not available for Nintendo 3DS devices. There are a lot of requests on the developer's forum and support pages as there was no plan to develop Skype application on the platform of yours. Keeping an eye on the future releases of this application is a good thing. No one knows for sure if it will ever happen but you will never know.
By default, Skype is available only for these platforms: Microsoft Windows, Apple MacOs, Apple iOS, Google Android, Microsoft Windows Phone, Linux and Blackberry devices.