Is there a specific purpose for the silver "swoosh" on Air Force One?
It's just for looks; an area of unpainted aluminum, polished.
In this close up you can make out the rivet lines and skin laps of the bare aluminum surface.  With a little work it's easy to get a finish like chrome plate, especially on a queen of the sky like that.

Back during American's natural finish paint scheme days, 80% of the fuselage was unpainted and polished.  AF1 just does it on a little patch so it's like a chrome accent.
There was significant weight saving in AA's case, but they finally gave in and painted their entire airplanes because the polishing has to be done regularly and is a pain, and over time the polishing, on an airplane that spends a lot of time outside and constantly re-oxidizes, slowly removes the pure aluminum cladding of the metal that is its corrosion protection.
Vinyl wrap is now starting to become common on airliners, and in theory you could probably do that sort of accent today with &quot;chrome look&quot; vinyl wrap, but AF1 has had that paint job for decades.