The health department in New York state did a retrospective of cases of babies who had a diagnosis that fit into vitamin K deficiency bleeding and those babies did not get vitamin k at birth the rate was 1-2 per 1000 babies. This is why they stopped allowing a simple waiver, and really the majority of cases they had were not even babies born to parents who objected to the vitamin k it was intentional or unintentional misses by the health care system.
There was a recent study published about the high rate of vitamin k Bleeds occurring in Thailand , turns out that maternal diet has an impact on if a baby has a bleed or not. The majority of the low vitamin k bleeds they had the mother ate less than the US rda 90 micrograms a day and the lower her diet was the higher the chance 50 micrograms or less a day was their highest risk category. Well it just so happens that 50 micrograms a day of vitamin k is the average amount a woman of childbearing age eats in America... So first off I would suggest you check your diet, there are a couple of online nutrient calculators (USDA nutrient data base and/or there is a neat tool at Self mag )
To address the oral, actually the typical flora that lives in breastfed infants, bifidus and other lactic acid forming critters do NOT produce vitamin K but they do consume vitamin K so if you increase vit k in your diet then more would pass into the milk and nourish the flora there . Mom probably needs to eat greater amounts of vitamin K than 90 micrograms a day perhaps to the dietary levels that seem to provide protection to older women 250 micrograms a day, that may improve the levels in breast milk. There are some small studies that show supplementing moms does increase the vit K content in their milk, we just don't have studies that show optimal amounts.
So oral K or the shot are stop gap things that are intended to prevent the bleeds we can't see like in the brain, if you do use oral vit k or get the shot then really it is not going to disrupt flora it will actually give it a boost since it is something the flora selectively consumes .,If you do give oral that comes in a mult-dose bottle it is in an olive oil base. Sometimes the give the shot contents as oral that has more things in it and I don't recall what all right now.
The rest of the info is more complex,and takes a bit of historical perspective in order to decipher. before they knew what vitamin k was , medical folks were noting and documenting signs and symptoms of vit K bleeds, we can read find some records from 1750's that talk about cases. In the 1890's Thompson in Boston figured out clotting time differences and noted a pattern that was different than hemophilia , he had around 50 cases and no successful treatments until this one 9 day old baby had a wet nurse and some bottle feeding and the hemorrhage stopped . So the oldest treatments were wet nursing(probably a woman who was eating herbs that promote milk production that were mostlikly higher in vitamin k) and goat or cows milk...so fast forward to the UK when they were not actually giving the majority of their newborns vitamin k, what they were doing was treating for Risk Factors - like premies and babies who's moms were on meds babies they resuscitated, or were bruised ....on top of that they had 3-4 day hospital stays and breastfed or not all babies got formula , do you see that this is exactly that old treatment feeding babies a replacement . McNinch said at that time the incidence was about 1 in 20,000 total birth population. but they had a sharp rise in incidence when they went to a strict breastfeeding only policy and the incidence of vitamin k bleeds was more often than 1-1200
(cuz this number also reflects total population not just breastfed infants that did not get vit k.)