Hi Neil,
These are the steps I followed in order to migrate my project.
1. Right click on the mbed project and select Export Program

2. Click on the drop-down list and select Kinetis Design Studio. Then click on Export

3. A ZIP file will be downloaded. Extract this file to a known location.

4. Open Kinetis Design Studio. On the Project Explorer region, right click and select import.

5. Select Existing Projects into Workspace and click Next

6. Click on Browse and select the location of the uncompressed folder

7. Make sure that your project is checked and click on Finish

After this your project should apear in the Project Explorer

Saludos
Santiago Lopez -- Connectivity and IoT