The dynamic balance of supply and demand in the labor market is a key issue at present. The change of employment quality is relatively complex. The current dynamic balance model of supply and demand cannot obtain high-precision evaluation results of employment quality and meet the requirements of practical application. Therefore, a dynamic balance model of labor market supply and demand under flexible employment is constructed. Big data network is used to set data acquisition channels, complete data collection, unify data sample format, formulate data processing flow, and obtain processed data samples. The correlation analysis method in big data analysis technology is used to complete the analysis of college graduation employment. This paper analyzes the relevant research work of employment quality evaluation, establishes the employment quality evaluation index system, collects the index data, normalizes the index data, then uses the grey correlation method to determine the weight value of the employment quality evaluation index, and uses the fuzzy c-means algorithm to establish the dynamic balance model of supply and demand in the labor market. The experimental results show that the designed method can better balance the supply-demand relationship in the labor market and has a good effect.