In which country is your card issued? FHR benefits and rates published on amextravel.com are specifically for USA-issued card accounts:
Every country that Amex offers card products in has a unique cardholder website and that would typically be where cardholders access FHR benefits. For example, Canadian cardholders log in through
https://www.americanexpress.com/en-ca/account/login. Once logged in, there's a dashboard where cardholders can navigate all of the card's offerings, including viewing and booking FHR hotels. FHR benefits offered in various destinations might vary slightly by the market where the card is issued, but based on what I have been able to tell from talking to US friends who also use the program, Vegas FHR benefits that are offered to Canadian cardholders are identical to those offered to US cardholders (they're just booked differently).