How do I build a report that sums up all 'Duration' days for designers across all projects for this year?

I imagine the duration information is in tasks assigned to designers across various projects. If that's the case, all you have to do is create a task report that filters based those assignments and your desired time period. Make sure you have Duration in the view and you select "Summarize this column by: Sum". Group by some date, like the planned completion date of the task. Group dates by year.

The report will be a list of all the tasks you want showing their individual duration, with the sum of all the durations appearing in the grouping bar at the top. Note that any parent tasks in the list will not have their durations included in the total, since they would already be counted in the sub-tasks. So make sure you assign designers to sub-tasks only and not to parent tasks.