We propose a microstructural model for the order flow in financial markets that distinguishes between exogenous core orders and endogenous reaction flow, both modeled as Hawkes processes. This model has natural scaling limits that reconcile a number of robust yet apparently contradictory properties of empirical data: persistent signed order flow, rough trading volume and volatility, and power-law market impact. In our framework, all these quantities are pinned down by a single statistic $H_0$, which measures the persistence of the core flow. The signed flow converges to the sum of a fractional process with Hurst index $H_0$ and a martingale, while traded volume is a rough process with Hurst index $H_0-1/2$. From these results, no-arbitrage constraints enable us to deduce that volatility is rough, with Hurst parameter $2H_0-3/2$, and that the price impact of trades is power law with exponent $2-2H_0$. With $H_0 \approx 3/4$, this model is not only consistent with the square-root law of market impact but matches remarkably well empirical estimates for signed order flow, unsigned volume and volatility.