That's an interesting circuit. I don't see why it wouldn't work even with the mechanical flasher.
Explain ".... when you turn on the blinker left or right the relay doesn't close as it should go from 30/87a to 30/87." Are you saying when you go to right signal, neither R-R1 nor R-R2 switch?
I can't see how "the brake lights work great and so do the turn signals" if the relays aren't switching.