Local flexibility markets (LFMs) are a market-based concept to integrate distributed energy resources into congestion management. However, the activation of flexibility for storage-based flexibility changes the respective state of charge. Compensation in later points of time is needed to regain the original flexibility potential. Therefore, we propose a LFM bid formulation including both flexibility and compensation. Furthermore, flexibility market participation might lead to inc-dec-gaming, i.e., congestion-increasing behavior to maximize profits. However, this inc-dec-gaming might lead to electricity market schedule deviations if LFM offers are not activated. We propose a risk-averse modeling formulation considering the potential non-activation of LFM bids to provide a framework for the assessment of LFM participation comparing different approaches. Our exemplary case studies demonstrate the proposed LFM bid formulation and show the impact of LFM participation modeling on inc-dec-gaming and congestion management costs.