Since Delcatty isn't available in the wild, you'll have to first get a shiny Skitty. The fastest way would probably be through breeding in the 5th gen with two parents from different language games - for example, an English Skitty/Delcatty and a Japanese Ditto, or vice-versa. The egg will have a 1/1366 chance of being a shiny!
Alternatively, you could look in the wild for Skitty in Route 116 in RSE or wait for a DPPt swarm on Route 222. Encountering wild Pokemon is much faster than hatching eggs, but the chances of finding a shiny are much lower (1/8192), and Skitty only appears about 2% of the time on Route 116.
Good luck and I hope you get your shiny Delcatty soon! :cer_smile: