Ken,
I found a little more info that may help locate the PCA Island No. 10 flag.
There are extensive files in the collection of donated material by David I. Bushnell, Jr. upon his death in 1941 and afterward by his mother Bell Bushnell (in 1946) to the "Manuscripts Department, Swem Library, College of William and Mary in Virginia." 4731 pieces of documents, etc.
One folder contains "Letters 1908-1916, some with the Smithsonian Inst. Correspondence" and another mention of correspondence with his mother (Mrs. Bell Johnston Bushnell).
I figure the correspondence of 1908 and 1909 may shed light on where the flag went.

But there are other references to "part" of, I suppose other documents, etc. in 1941 (bequeathed upon his death) and 1946 (from his mother) to the Peabody Museum of Archaeology and Ethnology, Harvard University, Cambridge, MA as we mentioned earlier.

As I mentioned earlier I checked with the Peabody Museum and they do not have the flag. I am sure you have already checked with the Smithsonian which D. I. Bushnelle, Jr. corresponded with often, and I know you checked with the VHS but has anyone checked with William and Mary College? That is, would the VHS necesarilly know what the college has?