This occurs when "Block Cookies" is enabled in Safari. To resolve the issue do the following -
- On your iPhone go to Settings
- Click on Safari
- Click on Block Cookies
- Select "Allow from Websites I Visit"
- Go back to the myFitnessSync - Fitbit to Apple Health app and sign in again
- Click on Safari
- Click on Block Cookies
- Select "Allow from Websites I Visit"
- Go back to the myFitnessSync - Fitbit to Apple Health app and sign in again