1. The way Brits (particularly Londoners) come to the USA (particularly New York because it's the shortest flight) to shop. This because the British Pound is so much stronger than the US Dollar, that it's actually cheaper to buy in NY than carry clothes from the UK, even including travel costs.
2. To bring nothing to a place and buy everything there.
Variant: "fly naked" = emptyhanded, without luggage or clothes
"It's so cheap, we are going to shop naked at Abercrombie and Saks!"
"we're flying naked to Orlando, they have great outlet shopping on International Drive"