Tom's answer is right on. I would also add that the "serious scrutiny" he mentioned in his post wouldn't just be from the aspect of a potential straw purchase.
If a private individual (i.e. not a dealer) shows a pattern of frequently buying and then quickly re-selling firearms, they'll probably also be looking at him for dealing in firearms without a license.
There's no hard-and-fast rule for how many guns is "too many", how quick is "too quickly", and how often is "too often", but like pornography, judges know it when they see it.