The models are stored in Google's Cloud and can't be downloaded.
Models trained in Prediction API 1.5 and earlier are associated with the user that created them - and cannot be shared with other users.
If you use Prediction API 1.6 (released earlier this month), models are now associated with a project (similar to Google Cloud Storage, BigQuery, Google Compute Engine and other Google Cloud Platform products) which means that the same model can now be shared amongst all members of the project team.