Enterprise routers assign queries to expert agents, yet deployed profiles stay static while agents evolve (prompts, tools, models), and developers rarely keep descriptions or exemplars current. We present FlyRoute, a self-evolving profiling framework that grows capability evidence from real traffic: dispatch candidates, quality-gate successful pairs into each agent's success store, periodically distill evidence into learned capability descriptions, and inject those descriptions together with BM25-retrieved successes into an LLM router. To make this flywheel data-efficient, FlyRoute introduces a targeted exploration policy that combines profile uncertainty, BM25 relevance, and lexical novelty, prioritizing under-profiled agents only for plausible queries and avoiding redundant evidence collection. In experiments on our proprietary enterprise developer-support dataset of real routed queries, FlyRoute improves a same-backbone zero-shot LLM router from 72.57% to 78.04% with only five seed queries per agent, showing that profile retrieval already strengthens cold-start routing. After streaming 7,211 labeled training queries through the flywheel, accuracy rises to 89.83% (+17.26pp over zero-shot; +11.79pp over cold start), with consistent gains across four expert domains under standard routing accuracy on single-gold test queries.