Diancie is a Legendary Pokemon that is obtained from Prof. Rowan after completing your Kalos Dex. You will receive Diancie in it's egg form - the egg will not break your shiny chain.
Diancie is breedable, with the EggGroup "Legendary". Diancie can only be bred with a Ditto to produce more Diancie Eggs. If the Diancie Egg is obtained from the Daycare, it will count for your shiny chain.
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Diancie can Mega Evolve with a Mega Stone if it's got a Mega Bubble on its summary page.