Will be interested to see robinhoods "financials" when they finally release them. It's likely their business model is of the "give free stuff away and raise more funding" variety.
Financials are not public but they make money like other brokerages i.e. on the float. They also seem to have a fremium model. Add to that other products they are offering and I won't be surprised if they growing in revenue per user terms. Yes, they are likely using VC money for growth but also have long term potential for a viable model