"Zillion billion" is not a real, defined number. The term "zillion" is an informal way to describe a number that's very large but not specific. Therefore, "zillion billion" doesn't have a concrete numerical value. As the reference indicates, "zillion sounds like an actual number because of its similarity to billion, million, and trillion, and it is modeled on these real numerical values. However, like its cousin jillion, zillion is an informal way to talk about a number that's enormous but indefinite."
In essence, "zillion billion" is used figuratively to emphasize a vast quantity rather than indicate a precise amount.