Long story short: unfortunately, no, it is not possible.
Dynmap works as it plugs into Minecraft javaclasses and thus has full access to everything. That is not the case with Factorio - mods have access only to a very specific APIs. In practice, there is no real way to communicate from outside Factorio to a mod dynamically, which makes any kind of dynamic map mostly a non-starter (that's also why things need to be pre-generated). I have some ideas of some hacky mechanisms to make it work, but I'm not sure that would give something really usable.
For the minimap - Factorio has no facility to export it. The Factorio binary has some options to export the map, but that's the bare geography, without anything (e.g., no trains), so it is not that useful.