A Glistening Coat is an item that is needed to cast Full Chemical Protection. One coat is consumed per cast.
You can purchase Glistening Coats (10,000,000 zeny) from the Alchemist Dealer (moonhaven 173 178) at the mall, which is on the left side of Moonhaven.
You can trade in one Platinum Coin for 2,000,000,000 zeny at the Coin Trader (moonhaven 199 193) using this process: Coin Trader > Purchase Zenies > Platinum Zenies. Then open your inventory and find the Platinum Zenies. Open it, and you will automatically be given 2 billion zeny. You can now purchase 200 Glistening Coats.