Error while installing Homebrew on Mac OS X (10.10.3): Unable to change file mode on /usr/local/
From your ls output:

drwxr-xr-x     5 root  wheel  uchg   170 Aug 20  2015 local

That uchg flag means the file or directory cannot be changed. You can remove it with this command: sudo chflags -R nouchg /usr/local

For more information about file flags, see the man page for chflags: http://ss64.com/osx/chflags.html