I spent an hour or so trying to do a random cone, with some frustration :-)
I should have used Gunter's model...

My attempt did not produce planar seam, but should have...

Probably best not to post my goofy attempt...

The "cone" apex of the outer frustrum is higher than the inner frustrum's apex.
The unwrap of the inner frustrum needs to be rotated a little, and moved a little...and offset by thickness...

Maybe cut the 3d solid frustrum, with a very tiny wedge, and Flow the solid to the outer frustrum unwrap???

- Brian

Edit, cut the solid frustrum in half with 90 degree cuts (?), and discard half, and Flow half to a flat, and then double it...???