The ribbon is the Asiatic-Pacific Campaign Medal. It was issued as a ribbon, like the one you have, starting in 1942. The full medal (like the picture above) was not awarded until after the war, beginning in 1947.

The two 3/16" bronze stars denote specific combat operations (there were 21 Army and 48 Marine/Navy operations) that your grandfather participated in during the war. The medal was awarded to any service member who served 30 days in the Pacific. Since you said your grandfather was in the Flying Tigers, one of the stars must be for the Burma Campaign (7 Dec 1941-26 May 1942)

There is another blanket "Air Combat" Campaign that lasted from 7 December 1941 to 2 September 1945, that could possibly account for the other star.

Sources:

Asiatic-Pacific Campaign Medal

http://www.skylighters.org/encyclopedia/apcm.html

http://www.tioh.hqda.pentagon.mil/Catalog/Heraldry.aspx?HeraldryId=15298&CategoryId=4&grp=4&menu=Decorations%20and%20Medals&ps=24&p=0

Pic http://imgur.com/vCKhbQC

Nother pic http://imgur.com/vlTymmL

Edit: does anyone know what the stuff even is?