The stock system relies on a certain voltage level to blink. In other words, the flash rate changes with the system voltage. When you rev the engine, the alternator assumes the load from the battery and raises the system voltage during recharge. I use the flash rate to tell me when the system voltage is low and the battery is discharging, kind of like an implied voltmeter.
Probably the first thing to check is what the voltage on the black wire to the blinker timer/relay is, compared to what is at the battery terminals. They should simultaneously be within 0.5V of each other with all other lighting on.
My first guess is that many of the connectors, fuse clips and switches in the path between battery and blink relay have oxidized, which increases the line resistance and voltage loss.
There are a lot of people that simply replace the stock relay with an electronic one which is not voltage sensitive and ignore the other voltage loss issues until something else goes wrong, with charge issues likely.
Another common issue is that some or all of the signal lamps have been changed from 1034 to 1157 and 1073 to 1156. These fit into the same sockets but have a different wattage, which changes the stock flasher cyclic rate.
Then there is the issue of proper and good integrity ground paths...