The wife said the dryer was sparking "in the back".
I moved things around, but didn't see anything so I tell the wife not to worry.

A week later, I turn on the 220v 3-wire dryer, and a single bright white spark
snaps in the back, between the dryer and the 4-foot 6-inch diameter aluminum
corrugated lint pipe connect to the outside vent.

Huh?

Could it be static electricity?
Could it be the dryer frame is hot?
What do I test?

The only connection to the wall is the three-pronged 220v dryer cord, which
looks perfectly fine when I remove it from the wall outlet.

There is no specific "ground" wire from the dryer to anything (should I have
put a ground wire in to the 120 volt outlet nearby?).

What would you test?
If you need pictures, just ask.