How to get Power Construct on Shiny Zygarde distribution in Pokémon Sun/Moon/Ultra Sun/Ultra Moon
1. Use the Shiny Zygarde code in Mystery Gift in your copy of Pokémon Sun/Moon/Ultra Sun/Ultra Moon
2. Pick it up at the Pokémon Centre and then go to Route 16 on Ula Ula Island
3. Get another 50% Zygarde. I got mine from Pokémon X/Y. It has to be one that has Aura Break. You cannot use one that has Power Construct because it cannot be broken down.
4. Take both the regular Zygarde and the Shiny Zygarde with you to the lab at Route 16.
5. Seperate the 50% regular Zygarde
6. Choose Assemble with Zygarde and Zygarde Cube and combine the cells with your Shiny Zygarde
Now you have Shiny Zygarde with Power Construct!