You should send token in http headers. Format:
Authorization: FlespiToken 45f73b59v345893456bhn345634576b9c3694
If your token is valid, try sending a get request using curl. But replace YourTokenHere with your token.
curl -X GET --header 'Accept: application/json' --header 'Authorization: FlespiToken YourTokenHere' 'https://flespi.io/gw/devices/all'
Also you can try to execute REST requests directly from the documentation.