The dev tools timeline can load external timelines by URL by passing a "loadTimelineFromURL" query param with the URL for the timeline.  This is used by tools like WebPageTest for embedding timeline views directly in the browser.

It looks like the URL passed to the timeline viewer is used without url-decoding so it is not possible to pass URLs that themselves contain query params.  I expect this is true for all of the query params handled by the Runtime in the inspector.

i.e. this URL: http://static.webpagetest.org/chrome/inspector-20160510/inspector.html?experiments=true&loadTimelineFromURL=%2FgetTimeline.php%3Ftest%3D160515_G4_TED%26run%3D2%26cached%3D0

Should load the timeline from /getTimeline.php?test=160515_G4_TED&run=2&cached=0 but in debugging the actual timeline loader code, it is passing the encoded string straight through to loadFromURL and is trying to load %2FgetTimeline.php%3Ftest%3D160515_G4_TED%26run%3D2%26cached%3D0

Passing the query param through decoded won't work because the &'s in the URL for the timeline file will pass through as separate query params and won't be included in the URL.