Play investigations after the relevant assassination

The point is only to get the achievement. You don't unlock anything by collecting them.

There are 4 achievements associated with flags:

1. Keeper of the lions passant - Find all of Richard's flags in the Kingdom
2. Keeper of the creed - Find all flags in Masyaf
3. Keeper of the four gospels - Find all flags in Jerusalem
4. Keeper of the crescent - Find all flags in Damascus

There is no continue option in the Animus since the story itself is over. You just jump back to a location in the memories section and continue finding flags, etc.

The best place to jump to is Memory Block 6, since from there you will have access to all areas of the map. You could also jump directly into an earlier memory and you will still have all your unlocked abilities and gear, but parts of the map will be locked.