I want to use these on my Flattop AR.
I have a #40 rear sight mounted.
A1 buttstock.
Will I need the High version to clear it,
or will the medium work?

( Haven't chosen a scope yet , but it will
 probably be a normal 3-9x 40 ,not a monster
 scope )

ARMS #22 High Rings.  Mounts the scope @ 1.450" center line.  These are 30mm rings, so if you use a 1" scope (not too many 3-9 mag scopes with a 30mm tube), you will need the inserts.

You could use the medium rings but it would require you to mount the scope in front of the #40.  You will mostlikely run into a spatial problem (run out of mounting room) on the flattop.  The #22 medium rings mounts the scope at 1.150" center line.  The #40 is .950" above the flattop.  This means the #40 will only be .20" from the center line of your optics.  This could cause a somewhat obstructed view.

Your best bet is the #35 Track Mount Base and #35 Medium Rings (It's $30 dollars more but worth it).  The base will give you another 1.13" of mounting space and the medium rings will give the scope a 1.250" center line off the flattop.  This system adds a bit more weight to the rifle, but is much more effective, IMHO.  

The centerline is the same 30mm or 1", the scope still sits in the midle of the ring.  Mediums are usually used if they are going on a 36 or 38 rail, high if they are going right on the flat-top.