Wikipedia: The Burke-Gilman Trail is a rail trail in King County, Washington. The paved, multi-use recreational trail is part of the King County Regional Trail System and occupies an abandoned Seattle, Lake Shore and Eastern Railway corridor. The 20-mile Burke-Gilman segment is managed by the City of Seattle south of NE 145th Street. The trail begins at 11th Avenue NW in Ballard and follows along the Lake Washington Ship Canal and north along Lake Washington. At Blyth Park in Bothell the trail becomes the Sammamish River Trail.
For FKT purposes, on the Golden Gardens side this route starts/ends at the terminus of the bike path at the official green sign that says "Burke Gilman: Begin." No need to cross the street or go all the way to the beach -- the trails over there are technically not the Burke Gilman. On the Blyth Park side this route starts/ends at the eastern most edge of the bridge over the Sammamish River.
I am making an unsupported attempt at the out and back today.