Coin flips -- specifically "games of chance" -- are used in rare circumstances at precinct caucuses to adjudicate ties or resolve issues created by rounding errors. At stake at these precinct-level coin flips is the one remaining slot in that precinct for a campaign to send a delegate to attend that precinct's county convention. Coin flips are not used to decide which candidate wins a state convention delegate or national convention delegate.
The Iowa Democratic Party does not have comprehensive records on how many coin flips/games of chance were held Monday evening. However, they do have partial records.
More than half of the 1,681 Democratic caucuses held Monday night used a new Microsoft reporting app. Of those, there were exactly seven county delegates determined by coin flip. The remaining precincts did not use the Microsoft app, and instead used traditional phone-line reporting to transmit results. In these precincts, there no are records of how many coin flips occurred. There's only anecdotal information on these precincts.
Who won these coin flips?
Of the seven coin flips/games of chance that were held in precincts using the Microsoft app, six of those were flips to determine whether a county delegate slot went to Clinton or Sanders. Of those six Clinton-vs.-Sanders coin flips, Sanders won five and Clinton one. The seventh coin flip was used to determine whether a county delegate slot went to Sanders or Martin O'Malley. Sanders won that coin flip as well. So in the seven coin flips that the Iowa Democratic Party has a record of, Sanders won six of them.
So it's incorrect to say that Clinton won every coin flip.
As for the less-than-half of the precincts that didn't use the Microsoft app, it's unclear how many coin flips took place. Only anecdotal information is available on these flips, such as web videos that circulated Monday night.
Did Clinton win the Iowa caucuses thanks to coin flips?
Clinton won the Iowa caucuses by the equivalent of about four state delegates. If the anecdotal evidence of Clinton winning six coin flips is correct, she would have won six county delegates through coin flips (setting aside the fact that party records show Sanders also won six county delegates as a result of coin flips). There is not a one-to-one correlation between county delegates and state delegates, or to national convention delegates.
Based on the party's delegate selection rules, a single county delegate represents a tiny fraction of a state convention delegate (the exact ratio is difficult to calculate because it varies from county to county).
Norm Sterzenbach, the former executive director of the Iowa Democratic Party who oversaw the party's 2008 and 2012 Iowa caucuses, told CNN:
"I can say with almost absolutely certainty this election would not have been changed because of the coin flips. It would take a very large number of these to make that kind of impact, and one candidate would have to win them all. Our empirical evidence and anecdotal information shows that one candidate didn't win them all, and that coin flips are not that frequent."
Sterzenbach has worked with the Iowa caucuses since 2000. He is not aligned with any 2016 campaign, has not endorsed a candidate, and did not caucus for any 2016 candidate.
He says that four state delegate equivalents may seem like a small amount, but that it would take "a lot" of county delegates to amount to four state delegates. Sterzenbach said based on his recollection, there seemed to have been more instances of coin flips being held in 2008 than in 2016.