An old saying goes ‘Mechanical problems take minutes to diagnose and hours to fix… electrical problems take hours to diagnose and minutes to fix’.
In other words - most of the time is in the diagnosis so if you can manage to do that yourself it will be done much more thoroughly and much cheaper than having a mechanic futz with it.
One thing you can do is use an old headlamp in place of the fuse that blows. I keep an old headlamp with a pair of wires and alligator clips for just this purpose. Connected to the line & load of the fuse location it provides a load if there is a short. In normal operation the lamp will be unlit. Excessive draw the lamp will glow. Dead short the lamp with shine brightly.
Now that you have stopped consuming fuses you can start to parse the problem. Several ways to do this - one would be to remove all 4 flasher bulbs and see what happens. If nothing, then replace them one at a time. If something then either test various parts of the circuit or disconnect the various parts - you will be trying to isolate the problem.
There is no one way to solve this but a methodical approach with notes on what you have checked (though it seems slow) is the fastest route to the answer.
Guesses on here and throwing parts at the problem are more exciting but can also be frustrating and non-productive.