The DJI SDK only works with DJI flight controllers. They most likely have their own over-the-air protocol that differs from MAVLink.
Unfortunately, as far as I know, your best bet is to use the MAVLink code generator to generate code for Objective-C or Swift. This is available here: https://github.com/mavlink/mavlink
That being said, it doesn't generate an easy to use SDK like the DJI SDK. You are going to need to spend a lot of time reading the documentation for MAVLink in order to know what messages to send, and when to send them. I'd advise you to take a look at the source code for one of the open source ground control stations that works with it such as this one: https://github.com/mavlink/qgroundcontrol