I’m not a iOS developer, so anyone please jump in and correct me if I’m wrong. But I believe in this case it’s unfortunate that iOS isn’t built on a paired down Linux. It’s built on a FreeBSD flavor of Unix, and Docker specifically requires a Linux kernel to run.
That said, I am very curious if it’s possible to somehow run a bare bones virtual linux machine on iOS for this purpose, somehow, the same way that it’s done on Mac OS X. My gut says that this probably falls under the umbrella of restrictions I’ve heard of for iOS, about not being allowed to include certain kinds of third party libraries within apps.
Sorry for my ignorance, but I’m also curious and would like to see this conversation move forward.