This paper introduces a methodology for simultaneously conducting multi-component 3D measurements in highspeed turbulent afterburning flames using several spectral plenoptic cameras. Traditionally, plenoptic imaging techniques capture the 3D scene using a single camera, where the camera is modified to include a microlens array that is located between the primary lens and the sensor. Each pixel behind a microlens encodes angular information onto the sensor by sampling a point on the main lens. A multispectral plenoptic camera is a combination of a plenoptic camera with a spectral filter array at the primary lens aperture plane. Thus, spectral information is encoded onto angular information, such that the camera captures spatial, angular, and spectral information of a light-field in a single-snapshot, which enables multiple measurements to be performed using discrete spectral bands from a single camera. Additional cameras provide improved performance by extending the overall range of angular information captured. Experiments were conducted using three spectral plenoptic cameras to capture subsets of the following measurement within a sonic hydrogen flame and subsonic ethylene flame: tomographic particle image velocimetry; dual-wavelength pyrometry of particle-laden flow; and 3D measurement the chemiluminescence of CH*. This work demonstrates the ability to simultaneously capture multiple 3D measurements with views from as few as three multispectral plenoptic cameras, whereas traditional cameras could require an order of magnitude more sensors.