There's no nonstop path between the Midwest and West Yorkshire, and that's the first thing to understand about business class from Kansas City to Leeds: every itinerary routes through a major East Coast or European hub, since Leeds Bradford Airport handles no widebody long-haul traffic. Delta typically connects via Atlanta or JFK before a transatlantic hop to London Heathrow or Amsterdam, with the final leg to LBA operated by a regional partner on a much smaller aircraft. American routes through Chicago O'Hare or Philadelphia into London, while United favors its Chicago or Newark hubs before positioning you for the transatlantic crossing. The realistic play, and what I always tell readers, is to book the transatlantic segment in a proper long-haul business product — Delta One's suite with sliding door on the 767 or A330neo, American's Flagship Business on the 777 or 787, or United's Polaris seat — and treat the final domestic-style hop to Leeds Bradford as a separate, short regional connection, sometimes even ticketed on its own to preserve flexibility.
Having flown this corridor more times than I can count, my insider tip is this: when connecting through Heathrow to reach Leeds Bradford, build in at least a two-hour buffer and land in Terminal 3 or 5 depending on carrier, since LBA-bound connections often depart from a different terminal than your inbound long-haul flight, and Heathrow's inter-terminal transfer during peak morning banks can eat 45 minutes alone. Manchester Airport, roughly 90 minutes by car or train from Leeds, is sometimes a smarter alternative connection point if your carrier's schedule aligns better there than at LBA, especially in winter when regional flights face more frequent delays.
Seasonally, January through March and again in October and November consistently offer the softest business class fares on this Kansas City to Leeds business class routing, as both leisure and corporate demand dip outside summer and the holiday crunch. Given how fragmented and hub-dependent this itinerary is, fares fluctuate more than on direct routes, so setting up automated fare alerts is genuinely the smartest way to catch a rare dip before award space or discounted business fares disappear.