It looks to me now that the bubble mailer could be considered a FLAT by the post office rules. Look at rule 2.3c here:
http://pe.usps.com/text/dmm300/101.htm#1002686

c. Flats less than 10 inches long that pass the test in 2.3a. and contain a rigid insert (see Exhibit 2.3c):

1. Place the piece with the length perpendicular to the edge of a flat surface and extend the piece one-half of its length off the surface.

2. Press down on the piece at a point 1 inch from the outer edge, in the center of the piece's width, exerting steady pressure.

3. Turn the piece around and repeat steps 1 and 2. The piece is flexible if both ends can bend at least 1 inch vertically without being damaged.
Exhibit 2.3c Flexibility Test—Flats Less Than 10 Inches Long

The bubble mailer is less than 10 inches long, and does have the rigid piece in it. And it seems to be able to flex that one inch and not damage anything. Looks good especially if not many chips inside and not overlapping. What do you think -- rule 2.3c ?

P.S. Note though, the flat rate is only about 50 to 75-cents less than the parcel rate.

Robert