Yes a flag claims a whole island. Place the flag on the island you want, put gold in it, ~20 mins or so later, it's yours. Press F1, place it, add gold, wait. After claiming you can adjust when your peace/combat timer is, but you can only adjust it once a week.
As for island points, it is based upon number of members in your company. With 6 members you should have plenty to claim a smaller island. The points are on the unclaimed island in the Atlas map. Smaller ones are usually about [37].
If the island is claimed, basically you can do the same thing to steal it. Press F1, place flag, add the gold, prepare for a fight.