While they don't have the particular book you're looking for, probably the most likely place that Fredric Brown's stories will pop up in DRM-free ebook (or ebook at all!) is Fictionwise.
Both Wildside Press and Wonderbooks Audio LLC (despite the name, they also do ebooks of Golden Age/classic 60s-70s sf/fantasy) have been releasing some of Brown's short stories and even his mystery stuff. I got the collection
Come and Go Mad when it came out just a couple of months ago. They'll probably get around to longer-length works at some point.
Here's the l
isting for his works available so far. There's currently a 50% discount coupon for Fictionwise, good for this weekend, posted right here in the Deals forum, if you're interested.