Rather than use Ajax / XMLHttpRequest / $http to invoke your WebApi method, use an html form. That way the browser saves the file using the filename and content type information in the response headers, and you don't need to work around javascript's limitations on file handling. You might also use a GET method rather than a POST as the method returns data. Here's an example form:
<form name="export" action="/MyController/Export" method="get" novalidate>
<input name="id" type="id" ng-model="id" placeholder="ID" />
<input name="fileName" type="text" ng-model="filename" placeholder="file name" required />
<span class="error" ng-show="export.fileName.$error.required">Filename is required!</span>
<button type="submit" ng-disabled="export.$invalid">Export</button>
</form>