Alas, it's not to be. Flex's SOAP implementation uses the
browser's HTTP stack, which means you need to set up client certs
via the browser. If that works for you, then it's relatively easy.
Just point your browser to the .p12 file, and it'll walk you
through the process. For me, this wouldn't work, since I was making
an app for general internet usage and I didn't want to have to have
all my users install the client certs.
Instead, I made a SSL proxy on a hosted server, and gave it
my client cert. It's a little kludgy and not the fastest thing in
the world, but it works relatively reliably.