How many shiny pokemon can one trainer catch in a single day before it would be questionable that the trainer may be cheating? [closed]

If this is a server-side mechanic as John Montgomery claims, it's unlikely there's any cheat detection for it. There may be checks in the code for bugs (I.e. the shiny function always returning true under some conditions because of some property of the RNG), but it's unlikely the user is going to be punished for developer mistakes. The server keeps track of all the pocket monsters, thus there's no way for a client to influence shiny rate.

Thus there's unlikely to be any check on the probability.

As an aside, millions of players play this game over billions of days of play. Thus it's elementary that someone will eventually get a one-in-a-billion shiny rate. As an aside, that rate would be getting 16+ shinies out of 51. The rate 5/51 or better has an 11% occurrence.