https://www.amazon.co.jp/b/ref=s9_acss_bw_cg_FFBE_1a1_w?node=5501173051&pf_rd_m=A3P5ROKL5A1OLE&pf_rd_s=merchandised-search-3&pf_rd_r=0CQ17P2V9Z8JJZMC7JJ6&pf_rd_t=101&pf_rd_p=f3516f40-c109-40a4-b6f2-16d83f087d54&pf_rd_i=5531218051

Event time: 3/14(0:00AM)-3/25(12:59PM) Japan time.

It looks like Android users who are using Amazon.co.jp's Amazon Android app store for the first time is eligible for receiving 1000 free Amazon coins upon downloading the game from the Amazon app store. The wording here is kind of confusing, but it looks after you download the game, you will get a discount coupon a week later via e-mail which you can use to purchase 1000 coins for free.

It also says that this offer is only for people currently living in Japan(I have no idea if you can use VPN to work around this). This also doesn't apply to people who has used Japanese Amazon app in the past or non android devices like Fire tablet.

I personally don't play the JP version, so I really can't be much of a help, but I figure I should post this so that people who are on JP can give it a try, or someone can make a guide out of it, like they did with the Korean One Store.

EDIT: Just to be clear you need to intstall Amazonアプリ/Amazon app, not Amazon ショッピングアプリ/Amazon Shopping App from the Google play store.