Identifying analyzable metaphase chromosomes is crucial for karyotyping, a common procedure used by clinicians to diagnose genetic disorders and some forms of cancer. This task is often laborious and time-consuming, making it essential to develop automated, efficient, and reliable methods to assist clinical technicians. In this work, an original label-free microfluidic approach to identify potential metaphases is developed that uses impedance-based detection of individual flowing nuclei and machine-learning-based processing of synchronized high-speed videos. Specifically, impedance signals are used to identify nucleus-containing frames, which are then processed to extract the contour of each nucleus. Feature extraction is then performed, and both unsupervised and supervised classification approaches are implemented to identify potential metaphases from those features. The proposed framework is tested on K562 cells, and the highest classification accuracy is obtained with the supervised approach coupled with a feature selection procedure and the Synthetic Minority Over-sampling Technique (SMOTE). Overall, this study encourages future developments aimed at integrating a sorting functionality in the device, thus achieving an effective microfluidic system for metaphase enrichment.