The evaluation of audio fingerprinting at a realistic scale is limited by the scarcity of large public music databases. We present an audio-free approach that synthesises latent fingerprints which approximate the distribution of real fingerprints. Our method trains a Rectified Flow model on embeddings extracted by pre-trained neural audio fingerprinting systems. The synthetic fingerprints generated using our system act as realistic distractors and enable the simulation of retrieval performance at a large scale without requiring additional audio. We assess the fidelity of synthetic fingerprints by comparing the distributions to real data. We further benchmark the retrieval performances across multiple state-of-the-art audio fingerprinting frameworks by augmenting real reference databases with synthetic distractors, and show that the scaling trends obtained with synthetic distractors closely track those obtained with real distractors. Finally, we scale the synthetic distractor database to model retrieval performance for very large databases, providing a practical metric of system scalability that does not depend on access to audio corpora.