WP REST API create post authentication issue

This is an old question, but the current REST API indicates that the X-WP-NONCE header should be set via the beforeSend callback. The following is directly from the REST API docs.

.ajax( {
    url: wpApiSettings.root + 'wp/v2/posts/1',
    method: 'POST',

    beforeSend: function ( xhr ) {
        xhr.setRequestHeader( 'X-WP-Nonce', wpApiSettings.nonce );
    },

    data:{
        'title' : 'Hello Moon'
    }
} ).done( function ( response ) {
    console.log( response );
} );

You can drop the headers property by doing the above, and using the contentType property. That is, if you use the $.ajax function.

$scope.formData = {}; //stores input from form above
$scope.processForm = function() {
        console.log(RestAPI.nonce);

    // using $.ajax not $http
    $.ajax({
        method: 'POST',
        url: '/wp-json/wp/v2/posts',
        data: $scope.formData,
        transformRequest: angular.identity,
        contentType: 'multipart/form-data',
        beforeSend: function( xhr ) {
            xhr.setRequestHeader( 'X-WP-Nonce', RestAPI.nonce );
        },
        success: function (result) {
            console.log('Success!');
        },
        error: function () {
            console.log('Fail!');
        }
    });
};