Unfortunately in Go there aren't really any methods. The best time to shiny hunt a Pokemon is when Niantic tells you to shiny hunt it.
Events are usually the best time to shiny hunt. Community days give you increased odds like 1/25. Events with increased spawns make it easier to encounter 450 of the species quickly.
Looking at weather in app is a good time to shiny hunt. When its foggy ghost types like Drifloon and Misdreavus are more common, also dark types like Sableye andHoundour.
Recently Niantic changed the algorithm of certain Pokemon so some Pokemon like Shellder, Caterpie, Snubbull and Nidoran female spawn more often in various weather conditions. Of course these spawns might differ based on biome.
Essentially the best thing to do is click on as many shiny possible Pokemon as you can. I've had shinies appear in less then 50 and also have had shinies take 1,000 encounters.
You might find a nest though Niantic has removed a lot of shiny possible Pokemon from nesting.
You can also hatch 7kms, even though shiny odds are 1/50 for baby Pokemon it still usually takes 150-200 eggs for a shiny baby. But I have 11 now.
Some Pokemon like Aerodactyl and Pineco have a higher shinyrate then 1/450.