Triangular lower studding sails, which didn't require a boom, were not unheard of. But I think it's far more likely that the Flying Cloud had lower studdingsail booms - at least on the foremast, and probably on the mainmast as well. (Studdingsails on the mizzen were rare, if not unheard of.) That sort of thing frequently gets omitted from models.
I gather the website you're talking about is the Drydock Models one. I don't take part in that site any more - since the operator of it outlawed (literally) plastic kits from it. But there are some nice models in the gallery section. That's all I know about that subject.
What I do have to question, in all honesty, is that little old Pyro kit. (As I understand it, we're talking about a kit that's just a few inches long - a member of the batch that I grew up thinking of as the "fifty-cent series.") I can't recall much about it, but most of the kits in that series are mighty basic, and a lot of them (probably not all of them) suffer from really major distortions in outline accuracy. Personally, I'd hesitate before putting much work into a kit like that. For one thing, the plastic masts and yards almost have to be way over scale in diameter, just to be practical as styrene injection moldings. And if they're shaved down to near-scale diameter they'll have a strong tendency to snap. My inclination would be to replace all of them with wood and/or wire. I think that series of kits was intended primarily as a means of introducing little kids with pocket money into the hobby. (They certainly had that effect in at least one case; I can remember my mother buying the "brig of war" and the Golden Hind for me at the local drugstore when I was about eight years old.)
On more than one occasion (most memorably involving the big, expensive Heller Soleil Royal - one of my un-favorite hobby products of all time) I've had the depressing experience of pouring a great deal of time and effort into a kit, only to discover afterward that it suffers from some sort of hideous inaccuracy that I didn't notice because I was so interested in the details. Nowadays my first move is always to compare the kit with a reliable set of plans. (One fairly common - and inexpensive - source we haven't mentioned yet is Alexander McGoun's The Frigate Constitution and Other Historic Ships. It's an old classic from the 1920s, and contains a rather basic, but decent, set of plans for the Flying Cloud. I've got a horrible feeling that they may resemble that little Pyro kit only in the vaguest sense.)
Unfortunately the American clipper ships haven't fared at all well with the plastic kit manufacturers. (By the standards of aircraft and tank kits, of course, no sailing ship has.) The old Revell Flying Cloud, from 1957, was a nice kit and is still worth acquiring if it can be found. (At all costs avoid its later, highly spurious incarnation in a box labeled "Stag Hound." The Stag Hound didn't look like that.) And many years ago ITC released a fairly decent model of the Sea Witch, which is currently being sold under the Lindberg label. So far as I know, those are the only plastic kits that meet a reasonable definition of scale models of American clipper ships. The situation is a little better on the wood kit front, where we have the Model Shipways Fllying Fish and the new Bluejacket Red Jacket (hmmm...I hadn't noticed the slight irony there before). Bluejacket, Marine Models, and A.J. Fisher used to produce some nice-looking, solid-hull clipper kits, but they're long gone. And the HECEPOB (Hideously Expensive Continental European Plank On Bulkhead) manufacturers have treated that type of vessel with their usual blundering contempt. It's really a shame. The American clipper, in the public mind, represents the ultimate perception of the sailing ship, but it's remarkably badly represented in the world of scale model kits.