1) I cut the envelope at the two ends so that I can open it like a page that has a fold in the middle.
2) When I add it to my signature I make sure it's going to be the center page that gets folded and that the white side is facing up.
3) Once the signature is attached in my book, I fold the envelope in the middle so that it conceals the stitch inside. The 'privacy print' (patterned side) is now the outside of the envelope. I add glue at the two ends, or the top and bottom of the 'page' to close it back up.
I sometimes just cut the flap off, tuck it inside or attach paper to it to create an extra journaling spot.