Did you order the OV-chipcard at the same time as ordering NS Flex on the NS website? Or did you first order your card at the OV-chipkaart.nl website and separately ordered NS Flex? If you ordered both in one order from the NS website the NS Flex season ticket should already be loaded on the card. If you ordered them separately you need to activate NS Flex at an OV-chipcard machine and load NS Flex on the card, without this last step NS Flex is not on your card and you will not get the discount. 

I ordered them separately. But I didn't any notification on the website which mention that I need to activate it on the machine and load on the card. It's not fair and logical that I paid for NS flex 3 months but charged full prices 

It is unfair, but this is how it works. On this forum there are similar questions like your nearly daily-most come indeed from foreigners, but also quite a lot from dutch. NS DOES mention this in the mail you always get when you change/start a subscription-only once you have loaded the new FLEX system this is later not needed anymore.

Also note that the 5/eur/month is only to give you discount when you checkIN in off-peak hours-there is on mo-fr both a morning and evening peak. This may also differ from what you expect or maybe are used to.

After ordering NS Flex (or other season ticket) you receive a mail with an order confirmation. In this mail it says you need to activate NS Flex at a machine.