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You need a full BB axle for two fixed gears.
No, if both gears are fixed and the same ratio, the split axle works. The "starting gear" kilo bikes had a low gear with a freewheel and a high fixed gear which was not fully threaded onto the hub at the start. After a couple of crank turns, the fixed sprocket wound onto the hub thread and bottomed out on the shoulder, engaging the high gear and causing the low gear to freewheel for the remainder of the race.
Except that bike wouldn't actually work for the kilo. You need a full BB axle for two fixed gears.