If you are both working on different files, you shouldn't have conflicts when you merge your branches together. Conflicts occur in git when it is not able to programmatically determine what change is supposed to be the one that ones during the merge.
For example:
In your branch, you delete a file. And in the other branch, your
coworker modifies it. So what is supposed to be there when the merge
is done? Should the file be deleted or does your coworker actually
need it in its new form? Hence the conflict. Git is going to ask
you, the human, to look at the change and decide what is supposed to
be there.
Conflicts are not a BAD THING. Proper organization of your branches will help to minimize them. But they are not something that you need to avoid. Resolving a conflict can be painful sometimes but it is not something that you should worry about. You can also minimize the risk of conflict through regular merging of your branches so that they don't diverge too far from each other.