Answer and Explanation:
To get the flimsy shovel recipe in Animal Crossing New Horizons, you can:
Give Tom Nook a total of 5 bugs and/or fish to invite Blathers to the island. Speak to Blathers the next day to get the recipe as a reward.
Buy the recipe from Nook's Cranny for 280 Bells after unlocking the shovel in the story.
Buy the flimsy shovel from Nook's Cranny for 800 Bells or from Wilbur on Mystery Islands for 100 Nook Miles.
Craft the flimsy shovel using 5 pieces of hardwood at a workbench.