Well you definitely have the hardest type of vent system to clean.
You will have to get up on the roof and clean it from there.
Trying to blow it upwards will just clog the screen on the roof vent.
Often it is the screen on the roof vent itself that is plugged but can also be in the pipe.
The really bad news is that most roof vents are not made so that they come apart for cleaning. so you have to get it apart in such a way that it is not destroyed and that you can re-install the screen etc. when you are done.
I usually end up with a bunch of minor cuts to my hands when doing these.
I will keep my fingers crossed that your vent will be easily opened up.
Once you get it open you could try to snake it with either a plumbing or electrical snake.
A check with a weight on the end may also work. I have heard that a good sized lock at the end will work.
You could try the same thing with a rope and a weight.
With luck bouncing the weight on the plug will dislodge it.
If you have a long enough peice of house wiring wire that may also work.
All depends what you have around the house that may do the job.
Be sure to put a plastic bag on the lower end to catch the lint.
Anyways to answer your original question there is no easy way to clean a roof vent system, at least I do not know of one.