Need to retrive WP rest-api using basic authentication

It depends on how you plan on handling authentication. My plugin does not handle any type of authentication out of the box.

If you can pass authentication information as query strings when doing the requests, you could use the jeherve_post_embed_base_api_url filter to add your own parameters to each request that is made:
https://github.com/jeherve/rest-api-post-embeds/blob/4bf9f0c79f784f4d0c6adaaf44879b2f08ad3d6e/rest-api-post-embeds.php#L153

If you plan on handling authentication differently, my plugin won’t be useful to you; you will need to find a different solution.

I hope this clarifies things a bit.