I would draw the flap as a rectangle, direct select the top corner anchor, hit Return and enter 0.125" Horizontal in the Move dialogue.
Then select the other top corner anchor, hit Return and enter –0.125" Horizontal in the Move dialogue.
I need to have the angle of the flap on this envelope mock-up be .125"
.125" is not an angle.
You need to explain what exactly you are trying to do. Your sketch looks like you want the "flap" of the envelope to be .125" in height. But your language suggests you want to maintain an angle, suggesting you want the angled segment to be .125" in length at its current angle.
And either way, .125" (one eighth of an inch) seems a mightly small measure for the flap on an envelope.