No, you do not need to load it on your card. When you ordered the subscription together with a new card on the NS website, the subscription is already loaded on the card. On the starting day it will be visible in your MijnNS account and you can use it from that starting day by checking in and out at the gate or pole at the stations. 

Thank you! Do you know if the subscription will be visible even before I take my first journey? Or do I have to do the first check-in in order to somehow activate it and see it on my account? Not sure if it makes sense...

You will probably receive another e-mail early on the starting date.

If you want to be sure beforehand, take you card to a service point (e.g. supermarket) and view the products on the card. If ‘Reizen op rekening NS (trein)’ is there (and most likely a second product for bus tram and metro), NS Flex is pre-loaded on your new card. It will probably show the starting date, too.

Alternatively, create a My OV-chip account at https://www.ov-chipkaart.nl/en then link the card and view the card details.

To my knowledge the subscription will become visible on the starting day somewhere shortly after midnight, say around 1 of 2 AM. This is done in the NS system and doesn't have anything to do with a check in. Everything that is needed for your NS Flex subscription is already on the card with a starting date and no activation is needed on your part. If you want to make sure the subscription is active, you can check your MijnNS on the starting date. You can also check your card on that day at a NS ticketmachine to see what product is on the card, that should be “Reizen op rekening Treinen”.