The only way to get the iOS dictation is to sign up yourself through Nuance: http://dragonmobile.nuancemobiledeveloper.com/ - it's expensive, because it's the best. Presumably, Apple's contract prevents them from exposing an API.
The built in iOS accessibility features allow immobilized users to access dictation (and other keyboard buttons) through tools like VoiceOver and Assistive Touch. It may not be worth reinventing this if your users might be familiar with these tools.