Outside of events like go fest, once they release a shiny version into the game will you always have a small chance of getting it if the pokemon is available?
According to this article, yes:
Once a Pokemon is made available as a shiny Pokemon, it is possible to receive a shiny variant in any way the Pokemon is obtainable. Evolved Pokemon cannot be caught shiny. They must be caught shiny in the basic stage, then evolved. The exception to this rule is Pikachu (and now Nidorina and Nidoqueen), who can be caught shiny.
It will always be in the game. For a while the way they introduced new shiny Pokemon to the game would be at the time of their corresponding event. You definitely have a chance to catch them even though it is a small one. Your best bet is to click on as many pokemon on the map as you see whether you want to catch it or not so that you can see if it is a shiny.