Sorry, but most pro software does not work on Chromebooks. Macs and PCs are typically used by designers, so supporting another platform that is not used by many professionals requires extra coding and support that typically isn't worth the extra expense. XD is not a web app, so it's not quickly ported to another platform. I would not expect to ever Chromebook version of XD. Just like other Adobe apps do not work on Chromebooks, nor does Sketch.
Adobe Certified Expert & Instructor at Noble Desktop | Web Developer, Designer, InDesign Scriptor