composer

a) Use this to remove a package from composer dependencies

composer remove asanchez75/phpflickr

b) Use this to add the following line

  "require": {
    "Jeroen-G/Flickr": "^1.0"
  }

to the composer.json

composer require Jeroen-G/Flickr

c) Use this command to update your composer dependencies

composer update

###########################################################################

{
  "name": "drupal/flickrgallery",
  "type": "drupal-module",
  "description": "My Awesome Module",
  "keywords": ["Drupal"],
  "license": "GPL-2.0+",
  "homepage": "https://www.drupal.org/project/flickrgallery",
  "minimum-stability": "dev",
  "support": {
    "issues": "http://drupal.org/project/issues/flickrgallery",
    "source": "http://cgit.drupalcode.org/flickrgallery"
  },
  "repositories": [
    {
      "type": "vcs",
      "url": "https://github.com/Jeroen-G/Flickr"
    }
   ],
  "require": {
    "Jeroen-G/Flickr": "^1.0"
  }
}

###########################################################################

If you want, you can add your github repo to packagist.org.
If you do not want, add this lines to your composer.json

  "repositories": [
    {
      "type": "vcs",
      "url": "https://github.com/Jeroen-G/Flickr"
    }
   ],