We examine the initial dynamical behavior of dissolving microbubbles composed of carbon dioxide gas in highly viscous silicone oils over a range of flow rates and pressure conditions. Microfluidic periodic trains of CO bubbles are used to probe the interrelation between bubble dissolution and high-viscosity multiphase flows in microgeometries. We investigate bubble morphology from low to large capillary numbers and calculate the effective mass diffusion flux across the interface by tracking and monitoring individual bubbles during shrinkage. The initial flux is characterized using a dissolution coefficient that reveals the influence of the oil molecular weight on the dissolution process. Our findings show the possibility to control and exploit the interplay between capillary and mass transfer phenomena with highly viscous fluids in small-scale systems.