The level of understanding of coal combustion compared to the requirements of predictive engineering is still insufficient due to the complexity of the processes and breadth of scales involved. In particular, in modern oxy-coal firing, where the fuel is burned in an oxygen/carbon-dioxide atmosphere to reduce the emission of greenhouse gases and pollutants, both experimental investigations and detailed numerical simulations are sparse. To understand and model the phenomena involved, the community follows a stepwise approach from generic to close-to-application combustion systems by steadily increasing the size, complexity and thermal power of the investigated burners as well as the complexity of the fuel. Here, an investigation of the flue gas of an intermediate range oxy-fuel burner is presented. To simplify the fuel in a first step, the combustion of methane in air and two oxygen/carbon dioxide atmospheres (oxy-fuel) is investigated. The concentrations of multiple species as well as the path-integrated temperatures are measured using three independent spectrometer systems based on tunable diode laser absorption spectroscopy (TDLAS). The rate of burnout and fuel-slip in the flue gas is studied through measurements of the concentration of CH4, whereas a quasi-simultaneously applied OH-measurement system allows for the detection of remaining combustion zones in the flue gas. An acetylene (C2H2) measurement as a chemical precursor provides insights to the formation of soot. The O-2-concentration is measured for an investigation of the oxygen-excess, and, in combination with measurements of the CO, CO2 and H2O concentration at various positions allows to detect the main components and pollutants of the oxy-fuel flue gas. An Allan-Werle variance is utilized to study the time scales occurring in the combustion process. A quasi-simultaneous measurement of the path-integrated H2O and CO2 temperature allows for investigating the progression of mixing of the different flows within the combustion chamber. This measurement reveals, that a complete mixing of all flows is only achieved close to the outlet.