Question:
When doing a self-pollination, do I need to trade pollen between flowers on the same plant, or should I use the pollen on its own flower?

Answer:
Genetically it shouldn't matter, because the pollen on all the flowers of one plant should have a very similar mix of gamete genetic diversity.

Hormonally, for two flowers of the same age, I doubt that the pollen would be distinguishable to them.

From a practical standpoint, it might matter if the pollen needs to be one age and the flower a different age for most effective pollination. In a case like that, if you trade pollen between 2 flowers of somewhat different ages, then one pollination will be more optimal.

I've done it both ways. Dale Borders, a very successful pollinator, used to trade pollen but now generally does not.

The Baker's pollination database does allow people to report this as a datum, that is, for selfings you can report: "Selfing-different flower same plant" vs. "Selfing-same flower same plant"... which means that when they set up the database they considered it potentially an important thing to record.