Traditional federated learning (FL) relies on a central aggregator server, which can create performance bottlenecks and privacy risks. Decentralized mix-and-forward designs remove the server, but repeated local mixing can attenuate global information under heterogeneity and expose peer-to-peer neighborhoods as a privacy attack surface. To preserve FedAvg-style aggregation semantics over updates reconstructable by the round deadline while scaling dissemination, we present FLTorrent, a BitTorrent-based dissemination layer for serverless FL with a short warm-up. Warm-up hardens within-round source unlinkability, a dissemination-layer goal orthogonal to content protections such as DP or secure aggregation, via pre-round obfuscation, randomized lags, and coordination-only non-owner-first scheduling with the tracker off the data path, before switching to vanilla BitTorrent swarming. We upper-bound the per-transfer attribution posterior by the fraction of owner chunks in a sender's eligible cover set, and derive a tighter high-probability bound that improves with early non-owner mass. A simple heuristic, GreedyFastestFirst, attains about 92% of a bandwidth-optimal max-flow upper bound, while warm-up remains a stable about 12% share of a round across 100-500 peers. Under an observation-only local adversary, FLTorrent drives attribution success close to neighborhood-level random guessing for typical nodes, improves with network size, and remains robust under collusion. In LLM-scale dissemination stress tests over 7-10 Gbps access links, FLTorrent adds only about 6-10% round-time overhead relative to BitTorrent-only. Overall, FLTorrent shows that within-round unlinkability and BitTorrent-level efficiency can co-exist with predictable, low overheads at scale.