Credenza issues, woodies advice sought  

Good question. The grain ...
Good question.
The grain shows that the face of the tambour is teak veneer. And from there I think the rest of the story tells itself, at least mostly. The builder must make a fairly conventional tambour door with veneer on the slats creating the invisible appearance. I am not sure whether the veneer would be cut beforehand with a guillotine, large format paper cutter, or other scissors like contraption, or whether it would be glued and then cut with a razor knife between the slats.
I think it would be difficult to cut it with a knife and not make a mistake especially with the grain pulling the knife around. So if I had to guess it is sliced beforehand and then individually glued to the slats.
I suppose it is also possible with the right substrate material, and the right guillotine, you could veneer a sheet of substrate and then chop the slats.
Probably somebody else here knows just how this was done. But you should also be able to get more information from a close examination of the existing tambour.

Thanks, Leif,
I might guess some guillotine as well for a pre veneered panel. I don't imagine I'll ever have access to one of those. I suppose a very long shot would be that someone who just happens to have some old teak tambour doors they don't need will see this. Yeah, right.

I did this with solid cherry,
sawing slats 0.7 inch wide. But then you lose a lot of grain.
It all depends on how your wood is sawn at the beginning, which
wood you source. I would advise quarter sawn teak, so that you aren't
obligated to follow the pattern that much?

Just an idea.
I've never done anything like this before, and I think you're in for a challenge, but here goes off the top of my head:
Top-quality plywood for the slats. Baltic or ApplePly. Accurate machining and close tolerances are critical.
Somehow clamp the slats tightly together on a flat surface in their final configuration face-up.
Apply face veneer by whichever method most appropriate (no vacuum).
Remove from clamps and flip assembly over, veneered face down.
Slip a thin and slightly convex sacrificial strip underneath and parallel to the slats to slightly open the joints between (hopefully not not glued together) and slice through the veneer with a sharp blade from the back side.
Repeat process on the reverse side with appropriate canvas.
I'm not sure if a counter or backing veneer is necessary in this case and I'd recommend using a paper-backed veneer.
I'd also advise consulting a cabinet shop that veneers their own panels as the process seems ambitious even for a seasoned DIY-er.

Uh...
I actually do have a single teak tambour door panel. The grain might not work with yours and of course the dimensions might be off, too. I can give you measurements later today if you're interested.

I have cut a lot of veneer wi...
I have cut a lot of veneer with a paper cutter. Not very expensive. Ebay is littered with them. But probably the big box office store has one too. And I am sure it will cut your teak veneer strips.

Tktoo: regardless of how...
Tktoo: regardless of how this was done in a production environment with special purpose tools, jigs, and the like, would this not be fairly straightforward to do by veneering the individual tambour slats and then gluing them to the backing clothe? I can foresee the whole process without the need for any unusual tools, even tough it does require great precision and a lot of repetition.
Glassartist: can you pull the existing tambour out and show us some close up photos between the tambour strips?
Oh and I've been very satisfied with using a heavy silk and hemp blend fabric and titebond II to glue it on in the last tambour repair I did.

pic
here is a pic. Let me know if you need more. Looks like a single ply of Beech to me without saw marks or evidence of sanding, more torn than anything.
Spanky, by all means let me know the dimensions of yours, including thickness.

Which is what it would it...
Which is what it would it would look like if a big guillotine cut the slats out of teak veneered beech stock.
So, businesses that sell metal or work with metal have very impressive guillotines. I wonder if you could work out an arrangement to use a guillotine after business hours or something.

Oops, sorry-
mine is only about 24" wide (x 24" high, approx), so it would be for a different style credenza. I only unrolled it once to look at it and that was a couple of years ago!

Spanky
Actually I am impressed that someone had one at all. I appreciate your looking into it.
Leif, I believe as you do that the whole thing is sliced veneered. I will be scratching my head a bit.

maybe...
I just did a quick google search and I think the trick is to balance veneer mdf , then to use a router with a v shaped bit, and cut from the back just deep enough to cut thru the veneer. Some sites mentioned this is like miterfolding a veneer corner. We used that detail quite a lot in the millwork design shop I had been working. I'm not sure what kind of shop would do a small order like this, but I would think a CNC machine would get the best results... though I am sure the crafty Danes had no such thing when your cabinet was made!

pirx: If the backs of the...
pirx: If the backs of the slats have beveled edges and loose backing cloth between them, won't that encourage them to jam when pushed, and not line up right in general, which will destroy the seamless/invisible look?
glassartist: You could simplify individually veneering the slats with a trough-like jig that guarantees the veneer is perfectly aligned when you apply the veneer, then stack and clamp them in batches of 10 or so. Lacking a guillotine this is how I would do it.

Yes
Something like that is likely what I will have to do.
Pirx pilot, There is no bevel at all. rectangular boards with canvas on the back so the front opens when the door rounds the corner.