Store GravityForm data in phpmyadmin (mysql)

You can use something like below. Basically after form submission we get the data $entry extract the values we want (in the example $val1, $val2, $val3) then insert that data into the custom table with $wpdb:

add_action('gform_after_submission', 'save_to_my_custom_table', 10, 2);
function save_to_my_custom_table($entry, $form)
{
  global $wpdb;

  // update for your tablename (this assumes the table lives in same database as the other wp tables)
  $tablename = $wpdb->prefix . "my_custom_tablename";

  // grab from values from the entry
  $val1 = rgar( $entry, '1' );
  $val2 = rgar($entry, '2');
  $val3 = rgar($entry, '3');

  // basic insert
  $sql = "INSERT INTO `$tablename` (`val1`,`val1`, `val1`) values (%s, %s, %d)";

  // use a prepared statement
  $stmt = $wpdb->prepare($sql, $val1, $val2, $val3);

  // run the query
  $wpdb->query($stmt);
}

If you are wanting to connect to a database totally outside the WP app I think you might want to consider setting up an API for communicating between the two. In that case you can still approach this very similary. See below:

add_action('gform_after_submission', 'save_to_my_custom_table', 10, 2);
function save_to_my_custom_table($entry, $form)
{
  global $wpdb;

  // update for your tablename (this assumes the table lives in same database as the other wp tables)
  $tablename = $wpdb->prefix . "my_custom_tablename";

  // grab from values from the entry
  $val1 = rgar( $entry, '1' );
  $val2 = rgar($entry, '2');
  $val3 = rgar($entry, '3');

  // send POST reqest to API for other database
  $endpoint="api.example.com";

  $body = [
      'val1'  => $val1,
      'val2'  => $val2,
      'val3'  => $val3,
  ];

  $body = wp_json_encode( $body );

  $options = [
      'body'        => $body,
      'headers'     => [
          'Content-Type' => 'application/json',
      ],
      'timeout'     => 60,
      'redirection' => 5,
      'blocking'    => true,
      'httpversion' => '1.0',
      'sslverify'   => false,
      'data_format' => 'body',
  ];

  wp_remote_post( $endpoint, $options );
}