As long as the run for the exhaust vent doesn’t have a ludicrous number of turns in it, it should be pretty easy to do yourself as long as you’re reasonably handy and willing to spend a little money on the right tools. Given this is something you should do regularly, it’s worth learning to do it yourself. Here’s an example of a kit that would likely work fine.
For those of you talking about full-on duct cleaning services, you may be just simplifying the description of the work that’s done, but if the only thing the service you hire does is hook up the vacuum truck for a few hours, you’re getting ripped off. At one point, I worked for a restoration company that did duct cleaning, and a good service will snake all of the ducts with a special air tool which knocks the dust loose from the duct walls while the vacuum is running. (They go from room to room, removing the vent covers and running compressed air lines down the ducts.) A good service will also disassemble the blower on your furnace, take the squirrel cage outside, and pressure wash it. If they don’t use tools inside the vents, the vent walls will still be covered with filth no matter how long they run the vacuum.