One-line download SDK and install command for current user would be:
curl -L "https://docs.google.com/uc?authuser=0&id=0B1i4NDqKFLYJM3NlYnRhLXFfXzQ&export=download" |sh
Actually Dart could be run on Google Compute Engine instances as described on this article. There you also can find other details on how to configure GCE instances.
But the problem is that you need to recompile Dart, as SDK provided on Dart downloads page does not run on instances provided by GCE at this moment (Debian 7 and CentOS 6). If you will try, you'll get this response:
/dart: /lib64/libc.so.6: version `GLIBC_2.15' not found (required by ./dart)But when you want to have your instance up and running quick, probably you don't want to spend instance's resources on recompile as it will cost you additional money.
/dart: /lib64/libc.so.6: version `GLIBC_2.14' not found (required by ./dart)