The objective of this mission is to defeat the boss. There are also several houses that you can interact with. The dragon vein points will allow you to melt the ice on the frozen late for one turn, which can be used to deter the enemy advance. Also, you have to visit the villager houses to get a reward after the battle. You need to visit 3/5 houses to get the best reward. If you've let the enemies reach the houses, more reinforcements will come out from the visited house.
At the start of the second turn, Odin and Niles will arrive on your side to provide assistance. The second house from your position will be reached by the enemy so you can't do anything about it. Divide your forces to two; one will push through to the north while the other will cross the lake. Your objective is to reach the middle-north and the southwest house near the lake since these two will be most likely occupied by enemies after a few turns.
Niles and Odin are very good damagers so use them with care and prevent them from getting attacked up close by the enemy. Silas and Effie will be your main tanks in this battle though Effie's limited movement range can be a hindrance. Don't hesitate to pair her up temporarily with either Silas or Elise to extend her range and deliver her to her destination. Flora will most likely use her Freeze spell to disable a character's movement which can greatly hamper your advance.
Once you're able to secure three houses, you can rest easy and regroup to take out the remaining enemies then finally defeat Flora and Kilma. You'll also get 10000g from defeating Kilma.