Step 1: Materials
For the pole, I found this "LintEater" 12 foot extension pole, which comes in four sections, and appears to be made of something like a flexible fiberglass. It's pretty pricey, at $29, but it was the only thing I could find that was semi-rigid, flexible, and strong. Most other materials that were readily available, such as wood dowels, would break too easily.
One big plus, is the fact that it breaks down into sections for easy transport.
(Upon further inspection, this pole is a little too bendy. Luckily, there are four sections, so I will likely use 2 two-section pairs, and tape them side-by-side.)
I'm sure there are better options out there, but I was limited by time, and an availability of open stores. If you can think of a better idea, please post it in the comments!
Step 2: Lay Out the Duct Tape
Lay the strips adhesive side up, overlapping one edge. Continue overlapping tape strips, in this manner, until the combined tape is equal to the desired width of your flag at the base of the triangle (you could, of course, modify as needed for whatever shape of flag you wish).
Step 3: Lay Flag Pole Onto Tape
Step 4: Fold Tape Over
Step 5: Draw and Cut Out Your Flag
Measure the width of your flag (in my case, 11.5"), at this point, and place a mark at half this width (in my case, 5.75").
Complete the triangle shape by drawing lines connecting the top and bottom of the base of the flag to your midpoint mark, using a straight edge.
Cut along the two lines you just drew to create the pennant shape.
Step 6: Fin.
Attach it to your bike trailer, etc., and have fun, in complete safety!
I'm sure there are better ways to do this, and I welcome your suggested improvements!