Of course there is a custom to give a flower to person who you know or in love. However, there is no custom to give a flower to a shop which is newly opened.
In Japan, when a store, restaurant, diner or any kind of local business opens except offices, friends or business partners send flowers to the newly open store/restaurant for the opening celebrations. These flowers are not the flowers which ballet dancers receive on their stages but bigger one and usually include a flower stand.
The type of flowers are mainly orchids but can be other seasonal flowers. Then, friends and business partners usually ask local florists or online florists to deliver these flowers to the stores/restaurants. Then, flowers usually come with notes that mentioning the names who had sent those flowers.