Answer

Although the chimney has a "bend" in it, the bend should have the same total square inch volume as the straight runs. I assume you think you can not use brushes because of the straight rods they thread onto will not pass the bend. You can use rope & chain. Wiggling the chain with thread the chain aronund the bend. Use 10 ft of 3/8" chain, tie a stout rope to the chain. From the roof, send the chain on down. Once it reaches the bottom, wire the chimney brush to the chain and another rope to the brush at the end opposite the chain. Get a helper at the bottom (so he gets dirty, not you :), and from the roof start dragging the brush up. Have the helper pull it back down. Do this as a sawing action, up & down, up & down;scrubbing the liner. Continue until you have scrubbed the entire liner. If you start from the top instead of the bottom, the creosote that breaks loose will fall to the bend and you might not be able to get the brush past the buildup. Once you're done, start over and get all the loose stuff out of the bend.
A alternate method is to burn the creosote away with a hot fire. This will in effect start a chimney fire. They are dangerous because the high heat will send fire out of loose mortar joints in an unlined chimney, and the result at the top of the chimney is a shower of sparks like you've never seen before. You need a inflammable roof and surrounding landscape. I had a chimney fire in an unlined chimney once & had to run a bucket brigade to the attic where I poured water down all sides of the chimney until the fire was over. It took about 15 minutes. If you feel safe with this approach, do it at night- it is spectacular!
A third method which I have not tried is a "fire log" containing chemicals to remove the creosote.
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