Emotional support conversation (ESC) task aims to relieve the emotional distress of users who have high-intensity of negative emotions. However, due to the ignorance of emotion intensity modelling which is essential for ESC, previous methods fail to capture the transition of emotion intensity effectively. To this end, we propose a Multi-stream information Fusion Framework (MFF-ESC) to thoroughly fuse three streams (text semantics stream, emotion intensity stream, and feedback stream) for the modelling of emotion intensity, based on a designed multi-stream fusion unit. As the difficulty of modelling subtle transitions of emotion intensity and the strong emotion intensity-feedback correlations, we use the KL divergence between feedback distribution and emotion intensity distribution to further guide the learning of emotion intensities. Experimental results on automatic and human evaluations indicate the effectiveness of our method.