Federated learning (FL) encounters slow convergence due to data heterogeneity issues. Recently, generative artificial intelligence (AI) has showcased remarkable capabilities in synthesizing realistic data. To effectively address the challenges of non-independent and identically distributed (non-IID) data, this paper introduces a collaborative AI training framework that leverages generative AI to enhance the learning performance of FL. In this framework, heterogeneous edge devices (HEDs) identify specific data categories lacking in their local datasets and acquire these data from Generative AI Providers (GAPs). This strategy aims to improve the convergence rate of FL. However, HEDs and GAPs may be reluctant to contribute their resources to FL training due to self-interest. Therefore, an incentive mechanism is necessary to encourage their participation. We propose a reverse auction model to facilitate data transactions among FL training buyers, GAPs, and HEDs within the FL training buyer's budget. It focuses on determining winners and devising payment rules to maximize the FL training buyer's utility. This involves solving a 0-1 programming problem with two sellers (GAPs and HEDs). To tackle this, we use joint bidding and virtual seller pairs for analysis. We demonstrate that our method ensures truthfulness, individual rationality, and computational efficiency. Furthermore, we employ a one-side matching mechanism to approximate the optimal solution. We further investigate a strategy to analyze and allocate data based on variance, aiming to minimize non-IID issues in local data. Simulation results demonstrate that our proposed matching mechanism can effectively improve the computational efficiency, with the test accuracy differing from the theoretical optimum by only about 0.7%, and our mechanism can outperform the other greedy algorithms. Additionally, our data allocation strategy enhances the test accuracy by approximately 7% compared to existing methods.