.then((item, attachments) => {
    let promises = [];
    attachments.forEach(attachment => {
        promises.push(addItem(item, attachment));
    });
    return Promise.all(promises.map(promise => { promise.catch(e => console.log(e)); }));
})
.then(() => { return getIems(); })
.then(items => $scope.items = items);

function addItem(item, attachment){
    let url = '';
    return Upload.upload({
        url: url,
        data: {attachment: attachment, model: Upload.json(item) }
    });
}

public async Task<IHttpActionResult> AddItem()
{
    try
    {
        //Здесь логика проверки и сохранения файла
        return Ok();
    }
    catch
    {
        return BadRequest
    }
}

.then((item, attachments) => {
    let promises = attachments.map(attachment => {
        return addItem(item, attachment));
    });
    return $q.all(promises);
})
.then(() => {
    $scope.items = getIems()
})
.catch(console.error);