Best How To :

Ok, so I finally got this.

I did this:

1. Select file and store file in ng-model
2. Validate some stuff
3. Submit main model (The one owning the files I want to upload)
4. Upload file to endpoints /api/myentity/{id}/resumee, /api/myentity/{id}/dni and /api/myentity/{id}/picture. Where {id} is the id of the entity I just created in the previous step.

So the trick here is to execute two requests, one to create the entity and retrieve the id, the second, to just upload the file.

The code looks like this:

// This is called every time the user selects a file
$scope.selectedFile = function (files, doc) {
      if (doc === 'resumee') $scope.documents.resumee = files.pop();
      else if (doc === 'dni') $scope.documents.dni = files.pop();
      else if (doc === 'picture') $scope.documents.picture = files.pop();
};

// This is called when the user submits the form
$scope.upload = function (docname, url) {

      var file = $scope.stepThree.documents[docname];

      return Upload.upload({
        url: url,
        method: 'POST',
        headers: {'Content-Type': file.type},
        fileFormDataName: docname,
        data: file,
        file: file
      }).progress(function (evt) {
        var progressPercentage = parseInt(100.0 * evt.loaded / evt.total);
        console.log('progress: ' + progressPercentage + '% ' + evt.config.file.name);
      });
    };

And finally, the markup is this:

<div class="form-horizontal">
        <div class="form-group">
          <div class="col-sm-2">
            <label> Resumen Curricular </label>
          </div>
          <div class="col-sm-2">
            <button class="btn btn-danger" ngf-select ngf-change="selectFile($files, 'resumee')"> Seleccione</button>
            <p>{{stepThree.documents.resumee.name}}</p>
          </div>
        </div>
 </div>

Since no one commented on this approach/technique, I'll take this as the best way in the world to work with file uploads, angular and a REST API.