I have a live national dex in X/OR so, let me know what you need to finish, and ill hook you up.
Also the items you are talking about are the oval charm and the shiny charm.
The oval charm is obtained by completing the Kalos Dex (excluding Articuno, Zapdos, Moltres, Diancie, Hoopa, and Volcanion.) and speaking to Prof. Syncamore, and increases the odds of your pokemon creating an egg when left at the day care
The shiny charm is obtained by completing the national dex and again speaking to Prof. Syncamore (event pokemon not needed) and this charm increases the chance of shiny pokemon appearing in the wild (or in eggs).
So as mentioned Genesect isnt actually needed, but I went to the effort of collecting and keeping all 719 pokemon (hoopa and volcainian to come) so if youre missing anyone hit me up and ill send them your way