This paper introduces a learned hierarchical B-frame coding scheme in response to the Grand Challenge on Neural Network-based Video Coding at ISCAS 2023. We build our scheme on conditional augmented normalized flows. It features conditional motion and inter-frame codecs for B-frame coding. To tackle YUV 4:2:0 content, two conditional inter-frame codecs are used to process the Y and UV components separately, with the UV components coded conditionally based on the Y component. Moreover, we introduce adaptive feature modulation in every convolutional layer, taking into account both the content information and the coding levels of B-frames to achieve content-adaptive variable-rate coding.