E.coli bacteria come in a large variety of strains, some of the normal and helpful, others producing strong pathogenic toxins. The "flora" usually refers to the normal inhabitants present in a healthy bowel environment. Hence, you could say, "normal E.coli absent" or, as philgoddard suggested, "E. coli flora absent".
Absent (or reduced) they are, if they have been flushed out of the bowel by severe diarrhea, or if they have been overgrown and displaced by other microorganisms in an unfavourable bowel environment which may be caused by e.g. unhealthy nutrition or longstanding antibiotic therapy.

"Coliform bacteria", as you said, is a term used to describe the presence or absence of fecal bacteria in drinking water. These tests mostly involve biochemical rather than (more expensive and time-consuming) cultural methods, and cannot reliably distinguish between E.coli and other similar fecal bacteria such as Klebsiella or Enterobacter.