You would have been able to before, but not anymore, sorry.
>The short answer is yes, by deleting your save you can receive the mystery gift again as long as the promotion is still there (untli mid january I believe). You can delete your save by pressing up + B + X on the title screen. And yes you can do this to get as many torchicks as you'd like by trading them away to another game before deleting.
Hope I helped.