Magento 1.9 – Customer Login into Mobile App Using REST API

It seams to work fine for me.
I get the admin authentication screen.
I think you may have used thisthe authorization url http://magento.root/oauth/authorize instead of http://magento.root/admin/oauth_authorize.

See the examples provided in here.
There are 2 of them. One for admin access and one for customer access. Use the first one Create a simple product as an Admin user with OAuth authentication.

[EDIT]
Urls should look like this:

$callbackUrl = "http://foo.bar/test.php";
$temporaryCredentialsRequestUrl = "http://foo.bar/oauth/initiate?oauth_callback=" . urlencode($callbackUrl);
$adminAuthorizationUrl = 'http://foo.bar/admin/oauth_authorize'; //this is what you need.
$accessTokenRequestUrl = 'http://foo.bar/oauth/token';
$apiUrl = 'http://foo.bar/api/rest';

If you want to skip this authentication steps then you can use cUrl to submit those authentication form without clicking on button.

You can use following tutorial for cUrl: http://php.net/manual/en/book.curl.php

My point of view you need to implement these steps in such way that only once you need to create authentication token after that you can reuse it.

You can use rest.js to implment rest api calls from your mobile app. Refer below urls 1. https://github.com/cujojs/rest 2. https://spring.io/guides/gs/consuming-rest-restjs/

Thanks