Many of the 1980s Beacon Rock climbers viewed Flying Swallow as the highest quality climb on the crag (yes, better than Dod's Jam + Dastardly Crack, better than Blownout). The old Jeff Thomas guidebook mentioned a runout, but this probably referred to the 5.4 ledge traverse prior to gaining the Flying Swallow dihedral.
P1: climb any of Local Access Only, Reasonable Richard (best choice), or Black Maria. Continue right along an obvious ledge and belay at the base of the Flying Swallow dihedral (5.9, 100 feet).
P2: Stem the dihedral (crux) up clean rock with bits of red lichen, past a bolt to a ledge (5.10d, 75 feet).
P3: A remarkably clean and beautiful dihedral starts with fingers and widens to hands. Belay at the obvious ledge. (5.10b, 60 feet).
P4: A short dihedral with hand crack ends on the far left edge of Grassy Ledges (5.10a, 40 feet).
There is a variation to P3: another less clean dihedral just to the right. Although not as aesthetic as the standard P3, it's worth top-roping at 5.10b/c.
On the SE Face somewhat right of Free For All. Consult Tim Olson's guidebook for details. P3 of Flying Swallow is immediately right of P2 on Flight Time.
Take the usual Beacon Rock rack, including some RPs for the start of P2 (crux). There is a 12 foot runout past the bolt on P2, but the stemming is easier here.
Each pitch has fixed anchors (with possibly ancient webbing) and the route can be rappelled.