If so how does one keep their wrist down and throw flat or anyzer etc?
you should only be wrist down to the extent that the disc lies parallel to the forearm.
as for flat, anhyzer, etc. all these shots are BEST performed when the plane of the shoulders matches the angle that you wish to throw.
that is to say, to throw a pured 20 degree hyzer, at the reach back your right shoulder should be 20 degrees below your left shoulder and when you are facing the target (into the follow through) your right shoulder and arm should be 20 degrees above "flat".
for a 45 degree anhyzer, your right shoulder will likely be level (or slightly higher) with the left shoulder at the reach but at the faced up position your right shoulder will be lower than the left.