Well, the high beam flasher and the indicators are fed from different fuses. Which did you replace? Perhaps both? I think your car is late enough to have 4 seperate in-line headlight fuses, before that there were none, for legal and safety reasons. If so it may also have the seperate left and right earths, if not, please see my comments below.
Do the headlights and sdielights work, also tail and brake lights? Does any other electrical item, e.g. interior light, not work? What about the brake failure test lamp?
If the headlights do not work normally, main and dip, suspect the black earth wires at the bunch of bullet connectors behind the top of the grille. For safety;s sake I strongly advise always, on every version of the Mini, running seperate earths from the left and right lights to left and right earth points, not the single point normallu used, which is just plain wrong, because it is unsafe. One wire coming adrift kills all headlights, main and dip, and possibly kills you too, if it happens on an unlit road in a dark night. Been there, not in a Mini, in about 1971, and not forgotten the experience....
If the headlights and all other lights do work normally, I think you most likely have a double fault. Do you have a multimeter, or even a test lamp (just a small 12V lamp in a socket, one wire attached to earth, the other free to probe with, will do)?
A hazard switch that is faulty will kill the indicators. Sometimes it has just been knocked and is not in the fully off position. There is also a flasher relay, which when energised (green circuit live) connects the light green-brown feed to the indicator stalk to the light green-pink fron the flasher unit, so that the stalk switch has "flash" power fed to it when the engine is running. The same flash power (light green-pink) feeds the hazard switch which directly connects it to the green-white and green-red indicator circuits when it is operated. So the flasher relay, a 4 terminal device, is implicated if the indicators don't work, but hazards do. An in-line fuse (brown one side, purple-orange the other outgoing) controls the supply to the indicator and flasher circuit in its entirety. The top fuse in the box (incoming brown, outgoing purple) controls the headlight flasher.
You could possibly have a break in the brown (permanently live) feed, depending on where it splits to go to the two fuses, so check at the bunch of browns on the starter solenoid.