John, my system does not cycle the relay when the flashers are on, the relays chooses which side to flash and the flasher can is upstream of the relays. AND, to throw another wrench in the works, I have been holding back with this gem-I have an add-on 4-way vintage flasher wired into the same system and it all co-exists!
1957 Chevrolet 5700 LCF 283 SM420 2 speed rear, 1955 IH 300U T/A, 1978 Corvette 350 auto, 1978 Yamaha DT175, 1999 Harley Davidson Softail Fat Boy