Matrilineally basically means that the children will belong to the mother's dynasty. They will still inherit according to inheritance laws the same way as any children from a "normal" marriage. But since you can only continue the game with characters from your own dynasty, NEVER arrange matrilineal marriages for your male ruler. On the other hand, ALWAYS make sure to marry matrilineally if you are playing a female ruler. Same goes for your heir, obviously.
As for the little blue flag: It only indicates that a certain marriage will solidify an alliance. Hover the cursor over the flag to learn with whom you will be allied if you follow through.
I think LOL ... Thanks again....