In the realm of combustion and reacting flow modeling, the calibration of the kinetic model parameters often relies on experimental data. However, not all data obtained under different experimental conditions (pressure, temperature, equivalence ratio, etc.) hold equal weight or feasibility for effective model calibration. Consequently, experimental design emerges as an important topic in combustion kinetics, aiming at identifying the most informative conditions computationally. In this work, we built a Bayesian experimental design framework enabling the highly efficient uncertainty reduction of kinetic parameters and model predictions. Our contributions are 3-fold. First, inspired by previous works aiming at uncertainty reduction of prediction or selected parameters, we proposed two new optimization objectives via model linearization oriented directly to quantities of interest (QoI), parameter-oriented and prediction-oriented design, for uncertainty reduction of specific parameters and prediction targets, respectively. We conducted theoretical analyses to link Bayesian information gain with dimensionless sensitivity (referred to as impact numbers) and to demonstrate the necessity of implementing QoI-oriented Bayesian experimental design (QBED). Second, neural network response surfaces with both kinetic parameters and experimental conditions as inputs were applied to the experimental design so that a single unified response surface can provide fast, differentiable predictions under a wide range of conditions. It not only facilitates gradient-based design but also accelerates enumeration-based design by parallel computing. Third, we integrated the posterior approximation by linearizing response surfaces with gradient ascent for design optimization. Comparisons with the enumerationbased method demonstrate that gradient-based design usually has a higher average information gain, while enumeration-based design, when assisted by the unified response surface, shows a faster computational speed with acceptable suboptimality.Comprehensive numerical experiments were conducted on the ignition delay times and laminar flame speeds of methanol. Statistical analysis was performed to prove the effectiveness of our methods. The dynamic evolution of uncertainty reduction was unraveled and is well supported by the insights from impact numbers. The proposed method can finish one design-inference iteration in 0.5 s in the 3-D design space and 1.6 s in the 9-D space on an NVIDIA GeForce RTX 2080 Ti graphics processing unit. The QBED source code was made available online.