Any number of crisis situations can result in the closure of transportation routes. Highways and bridges can be broken up by earthquakes, washed away by floods caused by hurricanes, a sudden downpour, or the melting of snow in nearby mountains. Roads can be closed because trees have fallen across them, or power lines are down and lying on the ground. A broken water main, a leaking natural gas line, a fire, a bad accident, a riot or demonstration, a hazardous materials spill, or criminal activity in the area might disrupt travel along certain routes.
Because you can never know in advance what is going to happen, it's an excellent strategy to scope out the alternate routes to and from your home, your place of business, the schools your kids attend, etc.
During any kind of emergency, especially when evacuation of an area has been ordered by authorities, it is common for traffic to clot the main transportation routes. You want to be prepared to sidestep all that.
Explore your neighborhood and community. Discover the little-used back streets and alleys that can be used in an emergency. Check out dirt roads that skirt the community altogether. Make contingency plans for routes you can take in the event there is a disruption of travel on what you might otherwise consider the "normal" routes.
Another aspect of your survival transportation strategy is to consider alternate means of travel. A motorcycle or bicycle can take you through narrow passages where no car or truck can go. Wearing a backpack and having panniers attached to the bike can allow you to carry your 72-hour kit pretty easily.
There might be times when you have to dismount and carry your bicycle past a spot where riding is impossible. Wear hiking boots or trail shoes that will protect your feet and allow you to walk long distances, if hiking is the only form of transportation left.