Developments in vehicle automation and the shared economy call for new developments in routing flexible transport services. We propose a new type of insertion algorithm: an online dynamic insertion algorithm with demand forecasts. The performance of this algorithm is tested in a simulation model for a case study network in the Netherlands. When combining the new insertion algorithm with empty vehicle rerouting, 98% of passenger rejections are eliminated and travel and waiting times are reduced by up to 10 and 46% respectively, compared to traditional insertion algorithms. A sensitivity analysis tested performance robustness to variations in operational and demand conditions.