Is it allowed to display Palestinian flags during Muharram processions, especially on Ashura? Does it diminish the significance of the Flag of Abbas (as)?
You can display either flag, or no flag. Flags are optional.
Beyond that, if the Palestinian flag is being flown to show genuine support for Palestinians, it is good. If the Palestinian cause is being co-opted to support someone else's political or ideological agenda, it may be less good.
If the people at the processions see national flags as taking away from the sanctity of the processions, this could also be taken into consideration.