Beauty is in the eye of the beholder. I find the curly Hetchins grotesque - it looks like it has been rear ended where as the Flying Gate, to me, is a thing of beauty. I saw an original Baines' Flying Gate at the since closed cycle museum in Camelford and I was smitten. I found the TJ Flying Gate web site and found the prices be well north of my budget. I stumbled across one for sale in the CTC forums for £150. It had been converted into a fixed wheel bike and the gear lever bosses on the down tube had been hacksawed off. I bought it with a view of doing some fixed wheel cycling but found that it was not to my liking. I contacted Trevor Jarvis to enquire about a refurbishment and restoration to geared status, converting it to 700c wheels from 27" wheels and having it re-enamelled. He did a great job and I bought second hand parts to restore it to a geared version.I don't see it as exactly a thing of beauty, unlike, say, a curly Hetchins. However, a friend who owns an original Hetchins and a TJ Gate says that the former is a pig to ride whereas the Gate handles like a dream.
I'd read the hype about it being a comfortable bike and that the short chain stays making the rear end more rigid and providing an invisible 'helping hand' on ascents through more power being delivered to the rear wheel through less energy absorption by frame flex. My cynicism about the 'helping hand' was dispelled on my first hilly ride. It does get up hills easier than my identically geared Dave Yates' bike and offers a very comfortable ride on distances up to 200km. I've not ridden further than 200km so can not comment upon even longer distances.
I couple of years ago i managed to get a close up view of a Baines' Flying Gate and the rearmost stays on the original are much thinner than the Trevor Jarvis version.