I am writing to answer as many questions about the Kamakura shirt as I can as I am a major fan and have something like 12 already.
The knit shirts are great- they're a sort of homage to the oxford cloth button down and most people have no idea they are knit until I mention it. Everyone has complimented me on them. The pique knit shirts are not see through- as one writer on this site worried. They are a heavy knit and in some respects resemble the complex weave of a royal oxford cloth. There are a few models of knit shirt that are flat weave (like a tennis shirt or a jersey fabric) and these are semi- see through. These non-pique knits drape beautifully- much more so than the pique- which has a stiffness/heaviness to the hand. I am a 15 1/2 34 shirt, 40 regular jacket, and I can wear either the small or the medium in the knit shirt- the small I simply dripped dry with no drier and the medium I put in the dryer. Now both sizes are about equal. I will drip dry all of them from now on. They do shrink a bit in the dryer-- mostly in the length of the body, not around the chest or neck. Obviously, they are a specialty shirt- for summer, and for those who like a play on a classic. Oh- both types of knit shirts are slim compared to their regular cuts in cloth shirts. There isn't a tremendous amount to tuck in compared, for instance, to a Brooks Bros. shirt.
The button down shirts at Kamakura are a great fit for me-- I have an end-on-end button down and a pinpoint oxford cloth. They are probably not going to please the people who like their button downs to have huge amounts of extra fabric hanging off the sides and back. Similarly, they are not made from that kind of oxford cloth that feels like Kevlar and over time softens up to a heavy canvas. Instead, they are smart-looking, trim (though not Uniqlo or mod emaciated) shirts whose shoulder seams sit at your shoulders and whose collars frame your head distinctively. Their fabric is suited to this smartness; it's a medium weight oxford cloth and a fine, tight pinpoint. As for the shrinkage of the cloth shirts - I have noticed very little (and again, I have not been putting them in the drier.)
The Kamakura aesthetic seems most likely to appeal to two types: 1, those looking for a classic button down look that has been slightly distilled and sharpened by a modern eye, and 2, those whose interest in "Ivy" style centers on the late 60's (the Ivy boom rather than the more traditional years prior), when shirt makers like Arrow produced the Cum Laude line (slimmer, proportioned but not yet body-hugging, floppy-collared 1970's stuff.) They mostly carry the staples (blue, white, some tattersalls, etc, in oxford and pinpoints) and anything else has to be made to measure. They intimated to me that every season will additionally feature some new ready-to-wear specials, like the linen shirts they had this spring and the chambray casual shirts they have now (blue chambray and white heavy-duty oxford, actually).
As for their service, it is impeccable. I haven't been so taken care of in a Manhattan store since - well- never before. The store, by the way, is aware of their sizing issues and they are fixing the system.