Generally the interpretation of a flying stork is an announcement of conception. But if we watch the stork sitting nearby, some authors consider the dream as a warning of possible pilfering around us.
Dream dictionary: Stork dream meanings
…In a dream, a stork represents sociable and sharing people. However seeing a flock of storks gathering in the wintertime in a dream means a meeting of thieves and highway robbers, or it could represent the enemy’s army, cold weather, air pollution, or strong winds. Seeing a dispersed flock of storks in a dream is then a good sign for a traveller, or it could mean returning home from a business trip….
If you dreamed of the stork, then such dream indicates the new life and new beginning. The new beginning could indicate the new project or thoughts you have made.
To dream about the stork indicates mother instincts or father instincts. Some women dream about it if they wish to get pregnant and become the mothers.
If we see it flying in pairs, it announces increase in family or marriage. If it flies alone towards us, it warns us about the thieves.