Throughout the Dune novels I would like to know how many times Duncan Idaho is ghola'd (cloned) before he reaches Kwisatz Haderach status?
According to the Dune wiki:
At least one Duncan Idaho ghola features in every novel from Dune Messiah through Sandworms of Dune.
Because a few gholas survive from one novel to the next (from Dune Messiah to Children of Dune, from Heretics of Dune to Chapterhouse: Dune, and from Hunters of Dune to Sandworms of Dune), this means that four Duncan gholas are featured as characters in the novels. But the number of non-featured gholas is way higher than four.
I don't remember seeing a definitive count mentioned in any of the novels, but I have refrained from reading anything not written by Frank himself, so I can't vouch for that. Unless Brian and KJA provided a definitive number, I doubt you can do any better than guessing.
Since Leto II kept ordering gholas from the Bene Tleilax during his 3500-years reign, and, obviously, not every single one of these is mentioned, you cannot have a definite and accurate count. After Leto's reign, the Bene Gesserit kept using the Duncan gholas provided by the Tleilaxu for another fifteen hundred years, and again, an unknown number of them were provided. It's a total of five thousand years of Duncan gholas.
In God Emperor of Dune, it is mentioned that only nineteen of the gholas the God Emperor used died a natural death. Most of them rebelled and ended up killed by the God Emperor. This does not help much in getting an absolute total count, though.
If I had to provide an estimate, I would say anything between one hundred and fifty (a fairly optimistic average of about thirty years per ghola) to one thousand Duncan gholas (a more pessimistic average of five years per ghola). Not a very tight interval but that's what I can work from the data available to me.
The Dune Encyclopaedia provides an interesting alternative perspective on this.
Out-of-universe (approximately, anyway), the actual Encyclopaedia itself has 21 Idaho, Duncan entries. One of those is not a ghola, of course. The second and third entries cover the same person. So that's 19 gholas with Encyclopaedia entries. (No, they are not the nineteen who died natural deaths.)
In-universe, according to the Encyclopaedia itself:
The "Welbeck Fragment" indicates that prior to 13663 nine Duncans had suffered violent deaths and nineteen had died of natural causes. These figures are now known to be highly inaccurate. Leto II's diaries in the Dar-es-Balat hoard have already indicated that over twenty Duncan gholas failed to survive the first-contact interview with the Fish Speakers, and the initial survey of the diaries reveals that there were well over seventy Duncans delivered by the Bene Tleilax.
The same entry notes that the Duncan Idaho ghola of 13663 is the second longest lived on record, having lived for sixty years. 70 gholas over 3500 years is a mean lifespan of 50 years, of course. More than 70, and the mean is lower.
In the Encyclopaedia's universe, the in-universe answer is thus "We don't know, because we've discovered that there were a lot more than there were let on to be.". Although the Encyclopaedia is officially divergent from the later novels, where there are of course yet more gholas after the Encyclopaedia's Duncan-The-Last, it is a fair speculation that "a number that only the Bene Tleilax know" is the common in-universe answer.
Interesting tidbit: In the Encyclopaedia's universe, the Duncan Idaho ghola of 12301 is also a Kwisatz Haderach, who is killed by the Fish Speakers almost immediately. But you probably weren't allowing for that in your question. ☺
According to Idaho, he was cloned 'hundreds' of times. Note that by this point he has access to all of their shared memories.
Why did Paul’s son have the Tleilaxu provide him with my ghola-self, hundreds of me! for all those thousands of years?
Heretics of Dune
It is, of course, not clear whether he means two hundred or nine hundred, but we can at least place an upper and lower bound on it. Probably it's a few hundred.