The quickest way to the mission is to get in a Yalm, head to ICC, and fly east to Milky Way. Once you have arrived in Milky Way your compass should point you towards the plants. You can also use fixer grid exit 6-R.
Alien Plants in Milky Way
Milky Way - 1640x2567
Once you have found the plants, all that is required is to target a plant and right click the Seed Box in your inventory, which will update to containing 1, 2 and finally 3 samples.
Warning: Be careful as the flowers are surrounded by a cloud of toxic pollen that wounds you for 250 points of poison damage. Have your handkerchief ready.
Now that you have the full container, all you need to do is go and hand it to the alien mission handler.