How long would it take to evacuate 6.5 million people?

The red shaded area is the envelope of most likely paths.

First order approximation
Assumptions:

• There is one working school bus for every thousand residents.
• They are in good repair and can operate twenty-four hours a day
• There is sufficient fuel and drivers to operate them around the clock
• The average capacity per trip will be 50 passengers.  Note that the capacity of a standard school bus is 72 children
• All of the major cities between the inner and outer circles are four hours by road from Houston.  The inner circle is approximately 100 miles from downtown Houston and the outer circle is 250 miles from Houston

At 50 passengers a trip the bus must make twenty round trips of eight-hours each to transport its "share" of 1000 residents.

20 trips times 8 hours per trip is 160 hours.  160 hours is a little over six and a half days.

If the target destinations were to activate their buses then the number of buses would be doubled and the evac time would be halved to a little over three days.

If the goal were to move the residents to the 100 mile line then the turn-around time would be significantly shorter.  Essentially the Houston area buses could transport to College Station and the receiving cities would pick residents up there for final leg to the destination.  In that case the first order approximation for totally evacuating 6.5 million residents from the danger zone would take 2.5 days.

That assumes ZERO commercial buses are pressed into service.

That assumes that nobody would evacuate by personal vehicle.

That assumes that every single soul complied with the evacuation order.

That assumes buses operating at 2/3 capacity.

One snide commentor suggested that the fastest way to evacuate Houston would be to put out a Facebook post that an Alt-Right rally was going to be held in Dallas on Saturday.  Then Antifa would handle the logistics of shipping half of Houston's population out of the danger zone.  Just sayin'