This study provides an in-depth characterization of Jet-A1 swirled flames' dynamics using advanced decomposition techniques on high-speed OH* chemiluminescence images. Research conducted in a 300-kW combustor with global fuel-to-air ratios Φ = 0.36, 0.24, and 0.18 reveals dominant low-frequency components under ultra-lean conditions through statistical and wavelet analyses. Integrating Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), and Multiscale Proper Orthogonal Decomposition (mPOD) enhances understanding by detailing the energy and frequency of flame modal structures. Observations show that as Φ decreases, flame size and intensity reduce, while fluctuations increase, indicating a transition towards unstable combustion dynamics. Furthermore, the frequency and intensity of burst phenomena increase, particularly in higher modes, indicating the system's approach to lean blowout (LBO). The application of nonlinear time series analysis, including autocorrelation (AFC) and phase space reconstruction, to mPOD eigenvalues, detects early warning signs of LBO. At lower Φ, the ACF reveals significant and frequent bursts, indicating high instability and intermittent behavior. Phase space reconstruction shows distorted orbits with a spiral-like structure, characteristic of substantial damping and irregular behavior near blowout conditions.