I don't know about precise percentages, but during the time I worked in gun shops after background checks were implimented, I would estimate that the number of denials was less than 1%, with delays being somewhat higher. To the best of my knowledge, none of the denials were ever prosecuted although I asked local police and prosecutors to follow up countless times.
However... there is another number, even more imprecise, and that is the number of people who started to fill out the 4473 and then stopped and decided not to complete the form. I worked in all three eras -- pre 4473, post 4473 and post background check -- and in the post 4473 era there were many folks, more than the denials but still probably less than 1%, who would stop after one or more of the questions and decide against continuing the process. Some folks would start asking all sorts of legal questions such as "what does adjudicated mean?" or "does my conviction for xxx count as a felony?" After the advent of cell phones, there were people who would read the questions and call her/his lawyer for clarification and/or explanation while standing at the counter.
And then, of course, there are the cases in which the 4473 and/or background check stopped an individual from purchasing a firearm, but didn't stop their criminal intent. For example, the one that I remember the most and which still causes an occassional nightmare, is an incident that occurred my first day on the job working for a big box sporting goods retailer. I was still a student and I took the job because the guy who hired me said that I could work evenings and weekends. First day on the job, I show up all excited at 6:00pm as scheduled and said hello to my 3 fellow counter guys. I knew something was up; they were all bunched up snickering and whispering but I was trying to be friendly so I asked "what's happening?" They were all real casual like and urged me to go over to a fellow at the far end of the counter who was looking at crossbows. I did so and spoke with him at some length about crossbows and equiping one for the coming deer season. After a couple of hours or so, he decided to buy a mid range bow, a box or two of bolts, some practice tips and some broadheads. It was my first sale at the new job and while it wasn't about to set the world on fire, it was a nice sale. Once again, I realized something was up because the other counter guys were now snickering and laughing, pointing and guffawing. That's when they told me the guy had tried to buy a firearm, but stopped because of the questions on the 4473; and this was in the period before background checks. I just turned pale, didn't say a word to these people I now considered ignorant jerks, and went to speak with management. I explained the situation to management, that I sold this crossbow to a guy, who couldn't legally own a firearm and that I was concerned. Management listened politiely and then told me not to worry, nothing would come of it. He was probably just a novice, wanting to get into deer hunting and admittedly there were lots of folks in that catagory at the time. It didn't turn out exactly that way. The next day, Saturday, I arrived at work about 1:00 and there was a county sheriff's crusier there. Went inside and was immediately approached by management and 2 officers. They asked me if I would mind going with them to confirm that the crossbow used to kill a young woman was the one I sold to the "novice deer hunter" the evening before. He had taken her on a picnic in a park down by the river and shot her in the head at point blank range with one of the broadheads. The sales receipt was still in the bag in the trunk of the car. Of course, he was claiming it was all just a "horrible accident." Just thought you might like to hear about one case where the 4473 and even a background check, had they been in use, would not have prevented a murder. Thanks for reading.