As a little research shows Captain Kidd sailed on the Adventure, a 280 ton, 36 gun Galley with 23 pairs of oars launched on 1695 and to make this look like the Adventure would have required major surgery. A little more research showed this kit to be the Wappen von Hamburg (The name means “Coat of arms of Hamburg” and the coat of arms from the city of Hamburg is clearly visible in the fancy work on the stern) a German heavy frigate of ca 1660 in the Hanseatic period. The first thing I noticed when test fitting (will be doing a lot of that, it is a Lindberg kit!) is that the lower gun deck has sufficient light getting to it to show that there is no deck, just mounting platforms for the guns. 
Three solutions presented themselves; ignore it, close the gun ports or scratch up a deck. I can’t ignore challenges so 1 is out and maybe it’s my German blood (or maybe I’m just a bit bellicose) but when I build warships I like to show them with guns bristling all over (hence my lack of interest in modern warships) so option 2 was not gonna work, plus I need practice at option 3 so it got an .040 sheet deck installed. It’s not the prettiest (there are some gaps at the hull/deck joint) but it will serve it’s purpose. 
I noticed while sanding down HUGE ejector pin (maybe ram is a better word) marks that there was no plank detail on the insides of the hull so I used my draftsman’s dividers to scribe some, it’s rough but again it will serve it’s purpose. 
Next comes decks, once I figure the best way. I expect I’ll install each deck separately and paint and detail as I go. As always, comments and suggestions welcome.
Re: adding new decks
OK, it looks like you worked out the kinks installing the lower gun deck. Now just follow the same procedure on the others and the decks will look great. Instead of plastic sheet, I prefer to use thin aircraft plywood with deck beams underneath the sheet to give them some support. Then I plank over the plywood and stain the planks. Keep us posted with pix as you go.
BTW, I built this kit many many years ago when I was in high school. As I recall, the finished product isn’t too bad, for a Lindbergh .
Ed.
I covered a full documentation on the build of this model and you can see it here. I invite feedback to see what you think.
Donnie
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Ed, good idea for the decks but I don’t think I want to go too far yet. I’m just learning my way around with this build.
Donnie, got your email and have bookmarked your build, very nice work. Unfortuneately the links for the pics in your last post are broken.
Yikes
I will see what I can do about that. I must have changed some images around.
Donnie
Good work so far! (How did you measure the shape of the lower decks?) Looking forward to seeing more progress.
I’ve finally managed to acquire a copy of this kit myself, for about £8 on eBay (the current Lindberg issue of this kit is ridiculously expensive at retail here in the UK, around $30-35). It’s the 1980s Revell Germany issue of the kit, which is actually labeled as the Wappen von Hamburg, rather than the completely spurious Lindberg “Captain Kidd”.
Anyway, I have to say that I’m incredibly impressed by the kit. It’s definitely far beyond the standards of Airfix kits of the time, and at least comparable to Revell’s smaller ship kits (Bounty, Mayflower etc.) Other than the lack of lower gun decks (has -any- plastic kit of a multi-decked sailing warship represented the lower decks properly?), and some sink marks + flash, it’s hard to fault the kit. I’ve appropriated some of the figures (there are about 3 of each pose) for my current “Sovereign of the Seas” build. The scale isn’t an exact match, but it’s hard enough to find 17th century crew figures in this scale range. The guns and carriages are also very nicely moulded, and I might save a few of them when I build the kit (by modelling some of the gunports closed) to use in improving other kits.
Although, the kit I have was produced about 20 years before the Lindberg “Kidd” so the moulds could well have deteriorated since then, and Lindberg probably had lower quality control standards than Revell AG.
Is the La Flore (“Jolly Roger”) similar in quality?