In a nutshell, the book "Dressed to Kill - the Link Between Breast Cancer and Bras" by Sydney Ross Singer and Soma Grismaijer is a work of pseudo-science. It is not written as a serious scientific tome, but more as an infomercial for the non-scientific (and very afraid) public. Serious flaws in the manner in which they conducted their study prevent me from recommending it.
Here's my reasoning: Neither of the authors, Sydney Ross Singer and Soma Grismaijer, are trained as medical doctors, medical research doctors, statisticians, or epidemiologists. Their background does not, in and of itself, make them sloppy or poor researchers, but it does diminish their authority to speak on the subject of causation of breast cancer.
Two good measures of the quality and merit of authors' papers are the caliber of journals in which they publish and the number of citations of their papers. Neither of the authors has any prior publications in a scientific or medical journal that I could find searching available databases. This undermines their credibility as researchers in general.
The authors' premise is that wearing a bra promotes the development of breast cancer, and that those people who do not wear bras should have a lower incidence of breast cancer, all other factors ignored. They specifically imply a causal relationship between bra-wearing and breast cancer. They offer no evidence beyond a correlation between the number of hours a bra is worn daily and the incidence of breast cancer. Without the inclusion of any of their data or statistical methods, they are just blowing hot air. Causal relationships are much more difficult to establish than correlations, but are considered to be definitive as long as a rigorous scientific method is followed. Correlations are not nearly as indicative and, under the formalities of logic, are not acceptable as proof (North American and Northern European women have a much higher incidence of cancer than do women in less developed geographical locations, but it is not possible to say believably that living in North America causes cancer.)
The authors' statistical treatment of their obtained data appears to be flawed. They do not include their data, a detailed statistical treatment of the data, or a discussion of the statistical methods used in their book, marking the book as fluff science - not a source I would want to trust for information on something as serious as breast cancer. Ideally, one would compare two randomly chosen sets of people (bra-wearers / no bra,) holding all other risk factors consistent, and compare the incidence of cancer in the two populations. This is not what the authors did; instead they looked at bra-wearing patterns in two groups (cancer/no cancer). I consulted with a professional statistician about their statistical sampling methods, and we agree that there are serious problems with they manner in which they conducted their sampling. 1) The sample was limited to American Caucasian women who live in large cities (in and of itself, this is not a negative, it just narrows the ability of the study to be used predictively for women who live in different environments.) The authors made no mention of how they recruited the non-cancerous subjects for the study and only briefly mention how they met some of the cancer-diagnosed subjects for the study. 2)The participants were not tracked or controlled for many other risk factors for breast cancer - factors which could easily confound the sampling and the statistical results. 3)The participants in the study were not chosen randomly, and in fact many were recommended by friends. This can confound the data by introducing sub-groups into the sample, which the authors may not be aware of. 4)Some of the questions the authors asked to obtain their data were subjective in nature, and the answers to those questions were subject to the interpretation of the question administrators when they were recorded. The authors made no mention of the conditions under which the interviews were conducted, except to note that some interviews were conducted over the telephone. The conditions under which an interview is conducted can significantly affect the outcome of that interview.
Lacking any convincing reason to believe that the authors are otherwise respectable researchers, I can only conclude that this book, and the hypotheses contained therein, merits little consideration. Their hypothesis is tantalizing enough that I hope they follow this study up with a better designed study, which they may be able to publish in a peer-reviewed journal.