It seems that part of amazon aws servers are blocked in China, we cannot download brackets or extensions. It still not work even using a proxy and I don't know why.
Are you able to download Brackets Releases directly from github: https://github.com/adobe/brackets/releases ?
Most Brackets Extensions are also github repos. Try going to the Brackets Extension Registry list (https://brackets-registry.aboutweb.com/) but instead of following link to extensions download (which is on Amazon), try following link to Extension Author (on github), then finding extension repo directly.
@redmunds sorry for this late reply. We couldn't download it a few days ago, but there is no issue now.China is unbelievable, for reasons you know...