Real-time, high-speed flow classification is fundamental for network operation tasks, including reactive and proactive traffic engineering, anomaly detection and security enhancement. Existing flow classification solutions, however, do not allow operators to classify traffic based on fine-grained, temporal dynamics due to imprecise timing, often rely on sampled data, or only work with low traffic volumes and rates. In this paper, we present Seiðr, a classification solution that: (i) uses precision timing, (ii) has the ability to examine every packet on the network, (iii) classifies very high traffic volumes with high precision. To achieve this, Seiðr exploits the data aggregation and timestamping functionality of programmable dataplanes. As a concrete example, we present how Seiðr can be used together with Machine Learning algorithms (such as CNN, k-NN) to provide accurate, real-time and high-speed TCP congestion control classification, separating TCP BBR from its predecessors with over 88-96 % accuracy and F1-score of 0.864-0.965, while only using 15.5 MiB of memory in the dataplane.