The flash player package is available for amd64 (I think it's still a 32 bit binary, but it's available as an amd64 package). You just have to enable the non-free repository in your sources.list and install flashplugin-nonfree
In case you want/need to install an i386 package from the repositories, you do the following (as root):
dpkg --add-architecture i386
apt-get install package:i386
It should automatically download and install all the dependencies as it would do with any other package.
In case you simply want to know the dependencies of a given package, I think you would have to install apt-rdepends
. Info on how to use it here