Flash orders have lower commissions, and always give the best available price[1] to the buyer.

The mechanics: best asking price is 10.0 on INET, 9.90 on ARCA. You place a buy order on INET. INET is obligated to route your order to ARCA (where the cheapest price is available) rather than filling it at 10.0 locally, and you get charged 9.90 + routing fee [2].

If INET flashes your order, it gives an HFT trader on INET the opportunity to fill your order at 9.90. In that case, you pay 9.90 for the trade and avoid the routing fee.

[1] A better price may be available on a darkpool, but the exchange would not have routed your order to the darkpool since the exchange did not know about it.

[2] There are flags you can set so that your order is canceled rather than routed.