FYI, Most of the problems with "brachycephalic syndrome" seen in breeds of the head type do not have anything to do with the chest and lung capacity. This can happen as well, but that is another conformational defect that can happen with or without the brachycephalic syndrome problems.
Stenotic nares: pinched or small nostrils.
Elongated soft palate: Too much soft tissue between naso- and oropharynx.
Irregularly small trachea, larynx and epiglottis.
These are the primary issues with brachycephalic head conformation. I have seen many cases of airway reconstruction here for these issues.
Also, if these issues are kept in mind, these issues can be avoided while still having a clear breathing brachycephalic breed, though the selection against them is a constant and vigilant battle.
Diminished wind capacity/lung field can also add to the deficits of the syndrome, but is not exclusive to brachycephalic breeds. There are many conformational faults that can decrease lung capacity/field, but that is another thread...