Okay, I waited until I saw some reviews of various cases for my newly purchased Kindle Fire. And then I went and looked at some well-known retail stores to get a "hands-on" of available cases. After looking into the various options, I decided to purchase the AmazonBasics case.
To the reviewer that indicated it smells "bad" -- the smell is because you are dealing with REAL leather, not some man-made material. And yes, the smell (which is faint and not intense) will fade in time, especially as it is exposed to sun and heat which will dry and further "cure" the leather. Go into a really good men's leather goods shop, and it will have a similar smell -- it is actually a good sign of quality material.
Stitching is well done. Nothing more to say on that.
Flexibility is good, and it is also strong where needed. I have no issue bending the case back, and it actually is "hinged" in two places along the spine to make it easier to bend both open and closed. It is also stiff where needed, with solid backing behind the leather. I have little worry about normal activity resulting in any sort of puncture damage through to the Fire. It isn't bullet-proof, and I wouldn't suggest using it as a shield, but for the Fire it should prove more than adequate.
The elastic that holds the Fire is tight and it doesn't move around much once in, but like another reviewer, I would be more comfortable if they were set a bit further in. I suspect that they weren't because if they were in deeper, they would cover much more of the speakers, which would impair the sound.
The closure elastic is fine, and is much like that which you would find on a nice Moleskine-style book. It holds the case closed firmly, and is set far enough in it is unlikely to come undone. There is some potential concern over this elastic wearing out over time, but I don't think that is significant unless you are constantly using it.
The interior is soft and should not cause any concern over scratching the device.
Now, for the stand function. This is perfect; it has three grooves that give a good variety of angles, and the grooves are deep enough to ensure it stays in place with all but the most severe attempts to dislodge it.
Is there a better case out there? Perhaps, but certainly not for this price. And from what I saw, I have yet to find one even at $40 or more.