Tenerife rarely appears on business class itineraries out of Central Texas, which is precisely why the routing deserves attention: there's no nonstop, so booking business class from Austin to Tenerife means constructing a smart connection through Madrid, London, or Frankfurt, with total journey time landing around 9.5 hours of actual air time plus a layover. Iberia via Madrid is the most natural pairing, since Iberia operates the Tenerife leg extensively and their long-haul A330s and A350s out of Madrid feature fully lie-flat seats in a reverse herringbone configuration. British Airways through London offers their Club Suite product with direct aisle access on select 777 and A350 aircraft, while Lufthansa routes through Frankfurt, where their A340s and A350s still largely run older Business Class seating rather than the new Allegris cabin, which hasn't been deployed on this corridor yet.
Having routed through all three hubs repeatedly, I'd steer travelers toward Madrid whenever schedules allow — Iberia's connection times at Terminal 4 are generous but not wasteful, and the T4 satellite building has a dedicated business lounge with real Spanish tapas rather than reheated buffet fare, a nice primer for the Canary Islands. My insider tip: fly into Tenerife North (TFN) via a domestic connection instead of TFS when weather is questionable in winter, since the south airport is more prone to crosswind delays that can unravel a tight Iberia connection — ask your booking agent about open-jaw options.
April, May, September, and October consistently deliver the best combination of fare value and weather, avoiding both summer peak pricing and the winter Canary Islands rush from mainland Europeans escaping the cold. Because award and discount business class space through these European hubs fluctuates unpredictably, setting up fare alerts for this specific Austin–Tenerife corridor is the smartest way to catch a rare release before it disappears.