JobScheduler - How do I determine a unique Job ID?

If I use a 3rd party library which also schedules jobs, does this mean I can't use the same Job ID as theirs?

Correct.

If so, how can I avoid these kind of collisions?

Ask the developer of the library what job IDs they use, or if those job IDs are configurable somehow.

If asking the developer of library doesn't work, you may want to calculate md5 on package name and pick last 4 bytes as unique id. The chances of collision will be quite less.