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I have found two places to obtain a Sakura flower, both are behind the green barrier in Valencia's forest.  There is one south of the starting point near the portal to the north pole and the other in in Tana's camp east of the starting point.  Both require Goddess slash to access so you have to finish either Mary's or Evelynn's story first and talk with Minerva before being able to finish Haru's story.  The flowers are sparkling as long as you need to grab one for Haru.

Mary's storyline starts by walking in on her before taking a bath three times.  Mary takes a bath in the evening in your bedroom.  Walking down into your bedroom in the evening is sufficient to count as walking in on her for these three times.  I recommend having at-least 3 charm (I don't know exactly how much you need for these but you'll need 3 charm eventually) before walking in on Mary the third time.

Mary gives you the task to find chickens again (this time in the center of town) later on in the storyline.  After walking in on Mary enough and talking with her a few times you eventually gain the ability to help her with the chickens during mid-day so check in with her during these times.  You might need some agility for this to trigger (I always get all my stats up to 3 before starting the NPC's storylines so I'm not sure).  The first time you help her out here you do a chicken chase but after that it's automatic and it trains agility.  You need to help her out at-least once more to advance the storyline.