I have this system https://www.kickstarter.com/projects/1621774283/battle-systemstm-sci-fi-modular-terrain . Would this work for a skirmish game or are those dependent on the core set maps tiles?

The skirmish game uses the same map tiles as the campaign. But if you're just playing casual games with friends, you're welcome to use whatever kinds of maps you want.

The game does not require any elements from the included map tiles? I read there are objectives in the skirmish mode also and don't know if that will work well using other terrain.

There are mission tokens and terminal tokens that are assigned to specific parts of the map, but they're not actually on tiles.

Nice! I have wanted to integrate these two things dice Imperial Assault was announced!