We approached your question from several angles before zeroing in on some possible solutions.
A flourless cake (many of which are out-and-out lies and include a few tablespoons of flour) relies on eggs and other squishy ingredients to give it structure, and requires gentle cooking to allow the center to set before the outside becomes dry and inedible. Some recipes recommend placing the pan in a water bath, in which the cake pan is set in a larger pan, with water coming about halfway up the sides of the cake pan. This tempers the cooking significantly, because no matter how hot the oven is, the temperature of the water cannot rise above 212°F (100°C). Putting the pan of water on a lower rack under the cake pan would defeat the purpose and leave the cake completely at the mercy of the much hotter oven air.
Putting a springform pan in a water bath does indeed present problems. Someone on the staff here suggested that it is all a question of the quality of the springform pan. A good pan wouldn't leak, this person said. So we asked the folks at Kaiser Bakeware, who make a line of high-quality springform pans. Their answer?"Our springform pans are not made to be used in a waterbath," a spokeswoman said. So that's out.
Now, we all know that if you have a large sheet of aluminum foil that covers the bottom of the pan completely and comes well up the sides, and as long as you are gentle enough with it and don't puncture it, it will keep water out. If you don't put a hole in the foil, the water won't come in. As a practical matter, though, we've seen lots of recipes that call for you to wrap a springform pan with two layers of foil, so apparently they know how rough you are and that you are likely to cause a leak. It does work; we've used it ourselves, even though it is a bit of a nuisance and mess.
Another solution is to find another recipe. We came across two online that address the problem in different ways. The first, Flourless Chocolate Cake, uses a regular cake pan, which is well greased and dusted with flour (or cocoa), and has a layer of parchment paper at the bottom of the pan, which is also buttered and floured. The cake is still baked in a water bath, but without the mess. Another option with an equally catchy name, Flourless Chocolate Cake keeps the springform pan but omits the water bath, and cooks the cake for 3 hours in a low-temperature oven (250°F, 120°C).
Take your pick, or sign up for that adult ed. class on the ancient art of aluminum-foil origami.