Identification of flutter margins in modern aeroelastic systems is a challenging task due to increased nonlinearities in novel designs, which can result in instabilities occurring below the linear flutter speed. These instabilities pose a significant risk as they may involve multiple stable solutions, such as large-amplitude self-sustained oscillations. The lack of efficient nonlinear bifurcation analysis methods for experimental systems exacerbates the challenges associated with postflutter analysis. This paper presents a data-driven method for predicting flutter instabilities and bifurcation diagrams of an experimental nonlinear 2-degree-of-freedom (2-DOF) airfoil. The approach uses measurement data from the preflutter regime to forecast the postflutter dynamics, eliminating the need for computationally expensive models. This study is the first application of the recently introduced data-driven bifurcation forecasting method to experimental aeroelastic systems. The results show that the proposed method is accurate, with predictions matching the measured behavior of the system. The presented study provides valuable insights into the nonlinear stability and dynamics of experimental airfoils and demonstrates the potential for applicability of this approach in the analysis of experimental systems. The findings have significant implications for online monitoring and evaluation of the nonlinear dynamics of aeroelastic systems in the aerospace industry, where safety is of crucial importance.