There has been a lot of testing done and your Search Level doesn't matter beyond a certain point, it could be at 999 and your shiny chances would still be as likely as 237.
But a few months ago a guy presented evidence that chaining doesn't actually work, that it's only the process of searching on the DexNav that increases the chances, so there is some hope for you there but you'd still have to be able to sneak over to them to not scare them, it just wouldn't matter if you did accidentally and broke the chain.
As for an actual chance? Most data seems to suggest 96th in the chain to be the average number but if chaining doesn't matter, then it's just 96 searches on the DexNav on average would yield a shiny.
If you're just encountering them wild by running through the grass, your chances are 1 in 8192