Can I configure advanced draft settings, like penalizing teams for keeping a player and deleting picks?

Yes. You can edit or delete any pick in your draft.

Note: For every keeper, Fleaflicker will remove a selection at the end of the draft. So if a team keeps a player, they lose their last draft pick. If they keep two players, they lose their last two selections, etc.

You can change this behavior by editing the draft order at League » Settings » Edit Draft Order » I want to edit the draft order round-by-round. Then select the owner's pick in the desired round and use the dropdown to the right to [DELETE] the pick or transfer it to another owner.