I don't understand. Either you record the result of the coin flip, in which case you can easily determine each participant's actual answer -- or you don't, in which case the data collected is useless.
An easy way to see this is if you suppose there's a question for which the truthful answer is "Yes" for 100% of participants. After the coin flip, you will get 50% "Yes" and 50% "No", which is the exact same result you would get if the truthful answer were "No" for 100% of participants.
Here's where I saw it. And yes, I admit sloppiness with my word choice.
"Differently from the usual Direct Response technique, in RR, respondents toss coins to determine whether they will respond to the question or just mark “yes”. This still allows admission rates to be calculated, yet it guarantees full anonymity to respondents because no one can tell whether an individual respondent answered “yes” to the question or because of chance."
An easy way to see this is if you suppose there's a question for which the truthful answer is "Yes" for 100% of participants. After the coin flip, you will get 50% "Yes" and 50% "No", which is the exact same result you would get if the truthful answer were "No" for 100% of participants.