I recently baked a rather sticky cake which called for a bundt pan. When I use a standard cake pan, I first put on the fat (either pouring oil and swishing it, or smearing butter with my fingertips) and then add some flour. Then I stand the pan in the position of a wheel and start turning. The flour gradually falls onto new, unfloured parts of the inner circumference and sticks to the fat.
When I tried it with a chimnied pan (actually a Frankfurter Kranz pan, but should go the same way with a bundt), no flour fell onto the chimney. No matter how I tried powdering the chimney, I found no way to move the pan so that the flour would distribute itself evenly. I then tried smearing the flour, but it stick to my fingers and the parts which stayed on the pan got overfattened instead of building a floury barrier.
What is a good technique to ensure that I have a nice fat-and-flour covering on the bundt? I am not asking about any kind of nonstick sprays, etc., just fat (solid or liquid) plus flour.