The purpose of this paper is to derive the Fisher information matrix for the Flexible Generalized Skew-Normal distribution (FGSN). Initially we derive the score functions which lead to the maximum likelihood estimators. We then compute the information matrix and consider the special cases corresponding to the skew-normal distribution and the normal distribution. We provide an algorithm to generate FGSN random variables and carry out a simulation to investigate the behavior of the estimators. The paper concludes with an application of the FGSN model which fits a real dataset.