If they only blink when the engine is revved up, you likely have a voltage issue. Original style flashers are voltage a load sensitive. Wrong bulbs do them in, as can voltage losses in keyswitch and fuse box assembly.
The flash rate can be band-aided by choosing a flasher that is neither load or voltage sensitive.
But, a lurking voltage loss in the system will likely just bite you later.
Find out how much your black wire distributes compared to actual battery voltage. A drop test like one probe on BATT + and the other probe on Black, will display a difference or loss. If over 0.5V, there is an issue to correct.
The same ought to be done the green wire to BATT-. The two numbers summed for total system error. The test conditions matter. The more load on the systems, the more faulty components will lose in voltage drop accross them. So have everything turned on for the test.
How your fuses blow can be another indication. True overcurrent and they will blow in center of the glass, as they are a bit thinner there. If they blow at the ends, it unlikely an overcurrent, but rather a heating issue of the fuse clips (oxidation) or back of unit connections (solder starvation). The clips can lose temper and not grab the fuse hard, also. Should need a pry tool to remove those fuses. They can be warm after a run, but, if they are hot enough to blister your thumb, there's your issue.
You've got some things to check...
Cheers,