What is the slowest highway speed you can drive?

Varies by state. Usually 0mph.

Usually states set their own limits just like they set their own speed limits. Also many if not all states will preempt a minimum speed if doing such a speed is going to cause a collision.

Samples:

Connecticut: 40mph minimum, preempted if congestion or traffic is ahead.

Rhode Island: Speed Limit-10mph, allows drivers to set speed limit based on road conditions.