The Brexit vote shocked Britain and the rest of the world, however, Britain's economy is not closely tied to the U.S. enough for this affect to be permanent. I believe that the U.S. stock market will recover within a month or two, but that Britain's economy will find itself in greater trouble in the months to come.
I agree that the U.S. stock market tumbled in the wake of the Brexit vote. However, I think the market will recover quickly. The stock market goes through fluctuations like this on a regular basis and always recovers. This is part of its history. The market has come back from much worse.
Britain is obligated to remain with the EU for a couple more years under the EU treaty agreement. It's a complex issue. Political experts are expecting it will take 10 years for Britain to start exerting its independence. The markets will likely recover quickly and remain stable for some time. Once Britain is free, there will be changes to the market. Hedge fund investors and other large investors will move funds around, according to which stock provides the best returns. Every time there is a change in global events, the markets tumble. The US will manage market fluctuations as usual -- the US controls half of capital flow on an international level and is accustomed to shifts in the market. These political changes could mean tough times for Britain and the EU economically.
There will definitely be a period of market turmoil, but the US stock market will recover quickly. Traders will be looking at the overall implications that the UK's exit has on the US economy, but ultimately the market will correct itself. It may take up weeks or months, but no more than a year for the market to recover.