The time zone identifier for Amsterdam is Europe/Amsterdam
and 1540688400
is the correct timestamp. There's surely an online tool to check but you can also verify it from PHP itself:
$date = new DateTime("@1540688400");
$date->setDateTimeZone(new DateTimeZone('Europe/Amsterdam'));
echo $date->format('r'); // Sun, 28 Oct 2018 02:00:00 +0100
However your code is not robust because depends on the configured timezone. You can just set it explicitly in a number of ways, e.g.:
$LoopDateTime = "2018-10-28 02:00:00";
$search_key = strtotime($LoopDateTime . ' Europe/Amsterdam') * 1000;
var_dump($search_key); // int(1540688400000)
Or:
date_default_timezone_set('Europe/Amsterdam');
$LoopDateTime = "2018-10-28 02:00:00";
$search_key = strtotime($LoopDateTime) * 1000;
var_dump($search_key); // int(1540688400000)
P.S. If I'm not wrong Sunday 28 Oct 2018 02:00:00 +0100 is the exact moment when most Europe has just switched from CEST (+0200) to CET (+0100).