Strictly speaking, SFAIK, this isn’t an official Northern Ireland Assembly Flag. AIUI, the Assembly has adopted a badge or logo; it’s six sprigs of flax flower. It has the same status in relation to the NI Assembly as, say, the crowned portcullis badge has for the UK Parliament, or the arms of Canada mounted on the crossed maces has for the Canadian Parliament.
Other parliaments don’t put their badges on a banner and use that as a flag but, such is the sensitivity around flags in NI, it has been judged wise for the Assembly to do this, and to use it as much as possible in preference to flags that might be more politically loaded or divisive.
So, yes, the overriding concern was to employ symbols that (a) had some arguable significance for Northern Ireland, but (b) had not hitherto been used in a way associated with one or other community (or even both communities - the red hand was ruled out both because it had been employed by loyalist movements and because it is the historic heraldic symbol of the 9-county province of Ulster, part of which lies in the Republic).
The flax flower refer to the linen industry, historically significant in Northern Ireland, and the six sprigs refer to the historic six counties of Northern Ireland (“historic” because they no longer function as units of local government).