teak crendenza tambour doors sticky, popping sound  

It could be that a stray bit of debris got inside somehow and is catching on the backing fabric or edges of individual slats as the seams open at one of the curved portions in the track. If so, you'll have to open the back (unscrews?) to access the tambour for thorough inspection.

The photos make it look like it has been heavily refinished. Perhaps there is some some teak oil between the slats? It is basicallly doctored boiled linseed oil, and if a bunch got between the slats in places, it could become a gummy mess that dries very slowly.

Also, oil could have gotten onto the fabric backing, dried it to hard and brittle and you are hearing resist bending and then breaking.

Really there are lots of things that could be causing the problem, so diagnostics are called for. As tktoo suggested opening the back would be a very good place to start. Hopefully Bernhardt Pedersen attached their backs in a fashion that

I agree with the above answers. I would go further to say, that if the sound decreases if you open and close the door multiple times, back to back, it is usually the result of the finish applied. As Leif was saying, when you oil tambour, some of the oil gets in between the slats. When closed, the slats are pushing together, and with some finish in between, you get slats sticking together. As it opens, these sticking slats are pulled apart, causing the popping sound. If this is the cause, it decreases with time. Unless of course you oil it again. I find it is mostly linked with resin content of the finish, in other words, Starbright teak oil seems to cause it less in tambour, than say Watco teak oil.