In order to get a random Flowersaur you need to buy the Fairy Bud in the Shop (section with a treasure chest) for 3 Flowersaur Talismans or 99 crystals. Seasonal Flowersaurs drop from the Fairy Buds only during their season. If you need a certain Flowersaur for your collection you can get it during special offer.
Available only during special offer:
You can also craft Flower Nectar in the Summer Kitchen or get them for free in the Snack Cart and Garden Gnome House.