Presuming an AONE3 as you want to do RTW in F but didn't have any place that you wanted to visit (so the AONE3 is the cheapest and still has a good routing), you can do lhr-hkg-nrt-hkg-dps-hkg-jfk-yvr-sfo-dfw-anc-dfw-lax-lhr-dxb-lhr-hel-lhr

Some of the flights are seasonal, so travel soon. DPS doesn't have F service most of the time but is worth visiting. And HEL is just for the hell of it (plus a nice contrast to DXB, always 100 degrees cooler than DXB no matter when you go). But after having done a few RTWs and drunk my weight in Krug, it really isn't such a great experience. Partly it isn't like it used to be, and partly there is a jadedness that sets in. Picking interesting destinations is more fun than picking interesting flights.