I'm using pulseaudio but I can get alsa to work as well. I think you could be hitting some issue where some version of portaudio you have installed wants to use the oss emulation which does not mix multiple sounds. Pulseaudio does a nice job of mixing though so maybe you should try that. You'l likely have to rebuild your espeak package though to link it against pulseaudio as I think the distros don't do that by default.
