People should do the right thing. But if they don't or if they don't even know what the right thing is, sometimes prices help.Sometimes prices help. Sometimes.
— Russell Roberts (@EconTalker) December 15, 2014
If you'll indulge me, I'd like you to consider for a moment what the underlying trade is here. Ignore the livery branding and what we have is a dangerous situation that bystanders need to flee—need in the sense that their BATNA could be disastrous if not fatal. Asking strangers to ferry folks away from danger is great, but unless you make it worth their while, consider that the answer might well be "no." Remember that most folks sensibly run away from danger.
If only there was a well-funded organization with the expertise and equipment needed to perform the dangerous task of evacuating civilians in emergency situations (apologies to Garett Jones). If only this organization already pre-selected for the type of people who intentionally run into danger. If only this organization enjoyed the sort of longevity encoded into the highest law of the land (Article I, §8; Clause 16), allowing for intertemporal resource allocation smoothing. You've probably already read the title of this post, so you know to which organization I refer. The problem with using Uber drivers to evacuate civilians in emergency situations is that Uber drivers are also civilians. They're generally not trained to deal with extreme situations, and they've not already pledged to put themselves in harm's way. Guardsmen have. Furthermore, your local armory probably has a deuce-and-a-half or two gassed up and ready to roll. The ARNG is the ideal organization for civilian evac.
Unfortunately, individual constituents are unable to invoke Title 32 mobilization by their lonesome. Only the governors of the 54 states, territories, and districts can do that (50 states + Washington DC, Guam, Puerto Rico, & the US Virgin Islands). So an app to call out for your local 88M to pick you up directly probably won't be forthcoming. But something to quickly and directly notify the governor's office is probably fairly reasonable. Think Yo, but with a few extra bits of information, like geodata, type of emergency, number of affected civilians, status of emergency (ongoing, etc). That sort of thing. By quickly crowdsourcing all the relevant characteristics of the emergency, supplemental responders can more rapidly coordinate an appropriate response.
If the problem is, "we need more people to run towards danger to help" then adding a surcharge to a peacetime livery service is one way to get there. But it ain't the only way. Before we set to thrashing Uber for their particular solution to a thorny problem, let's consider some other reasonable alternatives.