Rhythmic breathing is basically breathing in and out to the "beat" of your feet on the pavement. attendly.com/how-to-conquer... It's pretty simple really - although some articles can complicate it unnecessarily. It is just like dancing - where you take the weight on each foot in time with the music - if you try to do a Quickstep to the music of a Walz, then you aren't going to be a very good dancer.
I followed a lady at parkrun the other day - and I so much wanted to ask her to stop and then run with me for a while. She had over-exerted herself and I could hear that her random and spasmodic gasps for breath were in no way related to the rhythm of her running legs.