In Gen 7, the base chance is still 1/4096 and boosted to approximately 1/1365.
However, the most effective method in Gen 7 is SOS battles. The chance of finding a shiny Pokemon without the shiny charm is 1/1024. With the shiny charm, the chance is approximately 1/683 (rounded up). Putting each probability to common denominators, you have:
4/4096 (without charm) vs. 6/4096 (with charm).
Therefore, with the shiny charm, it increases the probability by 50% (1.5x). However, since we're talking about two still very low scales, you should really look at it as an increase from approximately 0.0977% to 0.146% chance (where both are still less than 1%).
Hope I helped! :)