Dryer vent cleaning can be a fairly simple DIY. Last year I bought a kit online, consisting of a brush and enough 3 ft rods for the brush to reach from outside to the bend in the duct just below the floor opening below the back of the dryer. The brush screws onto the first rod, and additional rods screw together as needed during the brushing. The end-most rod is driven by your own electric drill (variable speed preferred), in "forward" direction only. If the drill is run in reverse, the threaded connections come apart, and you lose brush and rods within the duct! With the dryer running on low heat (or air-only if the dryer has that), you feed the brush into the duct, drill running. Depending on how long the duct has been accumulating lint, you may get great gobs of lint blowing out the duct, so don't have your head in the exhaust stream.
Inside the house, after brushing out as much of the duct as can be done from outside, you can take take the duct off the dryer, brush the inside end of the duct, and then brush the duct inside the dryer from the exit end, but I wouldn't want the dryer blowing air out for that part. In my case, I got a fair amount of lint out of just the dryer. I also fished out an expired credit card (my son's), and a $10 Subway sandwich shop card. I have no idea if the Subway card is still valid.
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