Sears has 1/4" backer rod (you have to order it, as it is not on the
stores' shelves, here, anyway), so I would imagine 3/8" is available.
I know this because, recently, I ordered 1/4" rod. *I just happen to
have the invoice handy, here, and the part number is EF14C, item
description - 1/4" closed cell Backer Rod, 100 ft roll, quantity 2,
for a total of $20.90 plus tax and shipping. Maybe the 3/8" part
number is EF38C... do a Sears search.
Another alternative is to use 3/8" jute rope as a chinking medium.
You can stain the rope, with a dye stain (not an oil stain), to match
your color, dip/soak it in melted/hot wax, to make it water proof,
then insert the rope into the gaps. I would think waxed rope would
last longer than typical backer rod and be more readily replaceable
with itself, if ever pulled out. Pulling out "old" backer rod would
likely damage the rod, so you'd have to replace with a new rod.