I have had a quick look. The Singer study has never been published in a peer reviewed journal. You really can't take things seriously until they have. Other studies that have touched upon this seem to be uncontrolled studies with no accounting for related factors in the analysis. For example, it is entirely plausible that weight (and by extension diet)is correlated to breast size, and to whether a bra is worn. Obesity and diet are known risk factors in brest cancer. If you do a study proposing a new factor in the aetiology of a disease, you have to feactor out already known causes first. Show me a study that has done this, and I will be more likely to take the hypothesis seriously.

Also, the proposed causitive mechanism seems to be nonsense. It talks about the bra causing restrictions in the lymphatic flow. But the lymph in the breast drains at the back of the breast towards the chest, not at the places which might suffer constriction by a bra.