It is based on the number of fish minus 1 applied to a complex formula. The first chain, fish 2, reduces the chain effect more than the second chain which reduces the chain just a bit more and so on.
What I have discovered is that the shiny rate ratio loses about 45 percent on chain one (fish 2), and then there is a percent of each consecutive bonus added after each fish until you have removed about 95 percent of the ratio at about chain 38 or so. It will cease to be substantial quite early on, but you will have great gains overall. At fish thirty eight you are looking at about 1 in 120 Pokemon, vs about 1 in 128 or so at fish 37 and 1 in 140 or so at 36. It seems to be a matter of multiple infinites, with one infinite being larger than the other.