There is often a correlation between flow rate and E. coli concentrations. This may be due to the "flushing effect". That is, when it rains across the watershed, potential pollutant sources may be flushed into the river due to higher (surface) runoff form the land. You can imagine that during a heavy rain, E. coli sources (wildlife waste, livestock waste in fields, livestock waste in piles or on concentrated surfaces) could be mobilized and flushed into ditches or streams when there is high rainfall. Human waste may also be flushed into streams and rivers during high rainfall, depending on the system used to transport and process waste. In the U.S., some cities have what they call "combined sewage systems". Basically, the same pipes carry human waste and stormwater runoff. So, if there is a high rainfall, the system is overwhelmed, and waste is released into the receiving waterbody.
There is a competing idea in stream ecology: the "dilution effect", which is the idea that if the pollutant load is relatively constant, when you have more water in the river, the pollutant concentration is decreased simply by dilution.
Antecedent rainfall may be a substitute for river flow, if it is easier to obtain.
Agree with Dr. Mangiafico. In my Researchgate list, about 1998, we reported on the coliform issues in Stekoa Creek, and the effect to the Wild and Scenic Chattooga River. In general, even within the National Forests with constrained land uses, it is not unusual to find elevated to markedly elevated coliform associated with intense rainfall events and various non point sources. But point sources such as those found in Stekoa Creek due to exceeding sewer line capacity with storm water can add several orders of magnitude and delivered substantial distances downsteam, with some reductions due to downstream dilution effect. Note that care mentioned in obtaining adequate mixing in rivers can affect results, so sampling from the river bank, rather than taking multiple samples in the cross section can result in unreliable results. The USFS publication edited by George Dissmeyer on Drinking Water from Forests and Grasslands has some really appropriate papers on various water quality contaminants that can be associated with some of our best sources of drinking water. Its on the internet and I will try to add Later.