I wrote to Cornell Lab of Ornithology about the behavior and this is the response I got:
Hi Michelle, ? Very cool! ? Northern Flicker have an incredible suite of behavior related to courtship and aggression?and what you were seeing was actually typical for same-sex birds ? Here is some information from the Birds of North America online (http://bna.birds.cornell.edu/bna/) that I think will elucidate what you observed: ? Both sexes defend nest trees and mates aggressively. Agonistic behavior is highly ritualized in flicker ?dance? (Fig. 6). Typically, 2 birds of same sex pair off in mock ?fencing duels,? using their bills as ?foils,? while a member of the opposite sex looks on. This dance is prevalent during early phases of the breeding cycle (territory establishment, pair formation, and nest-site selection), but is also seen infrequently and at lower intensities at other times (Short 1982). Displays that comprise the dance are clearly agonistic (Noble 1936) and function in territorial defense, but territorial establishment and pair formation are so integrated in flickers that these displays may also play a role in pair formation; this remains poorly understood. ? Typically, 2 birds of the same sex face one another on a branch with their bills held at a slightly upward angle (about 30? from horizontal). Each bird quickly swings its head back and forth and bobs it up and down, such that the bill appears to trace a circular or Figure-8 pattern in the air (Kilham 1959, Lawrence 1966, Short 1972). The swinging and bobbing give the appearance of a mechanically animated toy, and are usually accompanied by in-rhythm Wicka Calls from both dancers. The red nuchal patch is usually erected in Yellow-shafted Flickers. Intensity of the dances varies greatly: the dance of 2 birds (same sex) is likely to have relatively low intensity and may even be silent, but the arrival of a third bird (opposite sex) immediately intensifies both the dance and the Wicka accompaniment. In very intense interactions, which are common, the dancers flick their wings and spread or rotate their tails such that the yellow, or red, ventral surfaces of the flight feathers are clearly visible to the opponent. Bursts of dancing and Wicka-calling might last 5?10 s, followed by a 30-s period of quiescence, followed by another burst of dancing where all participants seem compelled to join in. Bouts may last nearly half an hour (but usually are shorter) and may be joined and rejoined over a period of many hours. We have observed sustained series of dance bouts go on essentially all day, involving the same participants. Variation in the dance is substantial: the apparent context, number of participants, location, intensity, duration, whether the wings and tail are spread, whether Wickas accompany animation, pattern traced by bill, etc., can all vary. No data are available that demonstrate the range of variation or its meaning. ? "Dancing duels" often do not result in physical contact but instead one bird simply flies away. If one bird does not fly away after many minutes of dancing, the two rivals may peck and claw at each other and perhaps end up in a rolling fight on the ground (KLW). This usually results in a long period of one bird chasing the other, displacing it from perch to perch in short flights until eventually the "loser" flies away out of apparent exhaustion. ? You might imagine, these displays are more prolonged and intense during the spring.? To me this looks like one adult and one first-year female engaging? ? Thanks again for sharing!

Marc ?

From: Michelle Maani <lamoustique at yahoo.com>
To: "tweeters at u.washington.edu" <tweeters at u.washington.edu>
Sent: Wednesday, September 23, 2015 4:40 PM
Subject: Mating behavior of Northern Flickers and a question

I watched two Northern Flickers, going through a mating ritual which involved soft calls, head bobbing, and tail displays. This went on for quite awhile, over half an hour. At one point they did try to join. There was no mounting, it turned out to be a kind of an embrace.? (I have pictures of that sequence too but I didn't post them)
https://flic.kr/p/yY3wvQ
Wait a minute, you say, looking at the photo,? they both look like females. They do to me too. I'm not 100 per cent sure, the one on the left might be a male with extremely light malar stripes. Are they both females? ? After I sneezed and scared them into the brush, I could hear them continuing the behavior.? If you're wondering about this behavior in early fall, apparently the equal length of day and night around early fall causes a rise in hormones and some mating and courtship behaviors in birds.
Michelle MaaniVancouver, Washington