There is evidence that chest binding has a statistically significant impact on lung function.
A study  found that:
Transgender individuals using chest binders have abnormal lung function. The acute effect of wearing the binder appears to be an overall volume reduction with little other change.
 Cumming, R., Sylvester, K. & Fuld, J.P. (2016). Understanding the effects on lung function of chest binder use in the transgender population. Thorax 71. [Link]