I'm trying to work out if this sentence is correct, especially the usage of "having had seen".
He said he thought it having had seen my medical record.
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"Having had seen" doesn't make sense, in the same way that "he has had seen" doesn't make sense. The correct form is "having seen".
You can only do a very limited number of things with a past participle. One of the things you can do is turn it into a finite verb by putting "has", "had", "will have", etc. in front of it; another is turn it into a sort of participial adjective by putting "having" in front of it. Anyway, one of the things you can't do with it is turn it into another participle: even though "having seen" and "had seen" look like they might be present and past participles (compare with "having", "had" or with "eating", "eaten"), they don't act as such: you can't say "he is having read the message" or "he has had read the message", in the same way as you can say "he is eating the cake" or "he has eaten the cake". So "had seen" is not a past participle, and as such, you can't stick "having" on the front in the same way you can with "eaten".
I think a (thick) grammar book will do a much better job of explaining this than I will, so I refer you to any one of those.
The sentence seems to be describing three events which occurred in the following order:
If that is the case, then what is required is He said he thought it having seen my medical record. Without context, even that still isn’t very explicit, but what you probably need to note is that the construction having had seen doesn't occur in English.
You're trying to construct either a participial phrase or an adverb clause.
You can edit your sentence this way:
He said that was what he thought after seeing my medical record.
He said that was what he thought having seen my medical record.
He said that was what he thought after he had seen my medical record.
I think your construction "having had seen" is a kind of mix up of both participial phrase and adverbial clause.
P.S. I took the liberty of changing the wording in your independent clause.
As Barrie notes, "having had seen" does not make sense.
You could say, "He said he thought it, having seen my medical record." That is, because he saw my medical record, now he thinks it.
Or you could say, "He said he thought it, having had my medical record." That is, because he was in possession of my medical record, now he thinks it. (In this case having the record and seeing the record mean pretty much the same thing, as "having" in context would mean had it in his hands so he could see it. But in other context it could mean something very different.)
But "having had seen" ... doesn't really mean anything.
Take a look at this Ngram.
Having seen is the most common, as he had seen is quite rare, and having had seen is so unused that it doesn't even show. Having had seen on its own still doesn't register.
In short, having had seen is extremely non-standard. Hardly anybody says that, probably because it doesn't make any sense.