It does, but I swapped the chip in 2 dashes from identical cars, I am not sure that it will stop flashing if its from a later or earlier cluster, I did read on here that it did not for someone and I decided it was probably because the clusters were different (there are about 3 types, they look virtually identical). Still, if it still flashes but displays the correct mileage, you are at least better off than you were before. As its a different cluster its probably flashing because its a node on the system that was not programmed in by the factory and you will never be able to stop it flashing with software only with replacing the BC with one identical in everyway apart from the cluster which is unlikely or by putting in some sort of delay timer as you do to retrofit Connect Nav. This delays the unprogrammed node from being turned on until after the BC has done its checks which should prevent the mileage from flashing, whether this method will work with an instrument cluster, though, is unknown.
I ve edited your picture and attached, but I think the picture youve uploaded is from your car without the central LCD display because I have dismantled dashboards from 147s from 2002, 2003, 2004 and 2008 and none have a board quite the same as that and in the UK we only got cars with the LCD display. On the board in your pic there is nothing where chip 93c86 is on all the boards I ve seen, so It appears that cars without the central LCD have 93c86 in a different location, assuming they dont store mileage in a different chip altogether. Look in the same place on the board with the central display and you should find it, it has 8 pins, the writing is very hard to read, but at least if you find it you know what youre looking for on the board with the central LCD.