I am looking for the exact formula for the calculation of Fold Change (FC), p-val and q-val in Ballgown stattest?

By using gexpr I got the gene expression values for the list of genes. For better understanding I tried to calculate the FC for a few genes manually but the values I obtained differed from the values given by stattest. Can you please help regarding this?

From the vignette:

The default statistical test in ballgown is a parametric F-test comparing nested linear models; details are available in the Ballgown manuscript (Frazee et al. (2014)). These models are conceptually simialar to the models used by Smyth (2005) in the limma package. In limma, more sophisticated empirical Bayes shrinkage methods are used, and generally a single linear model is fit per feature instead of doing a nested model comparison, but the flavor is similar (and in fact, limma can easily be run on any of the data matrices in a ballgownobject).

Ballgown's statistical models are implemented with the stattest function. Two models are fit to each feature, using expression as the outcome: one including the covariate of interest (e.g., case/control status or time) and one not including that covariate. An F statistic and p-value are calculated using the fits of the two models. A significant p-value means the model including the covariate of interest fits significantly better than the model without that covariate, indicating differential expression. We adjust for multiple testing by reporting q-values (Storey & Tibshirani (2003)) for each transcript in addition to p-values: reporting features with, say, q < 0.05 means the false discovery rate should be controlled at about 5%.

If you want to know what you are doing, there is no substitute for reading the original manuscript.