"Are there yellow flowers blooming in the yard?"
I have the same question. Blooming is an action so it shoild be de, shouldnt it. Its not like the japanese sentence says rheee are blooing flowers in the garden. Instead it says the flowers in the garden are blooming.
I think it should as I hear blooming as coming into bloom since flowers don't bloom, the plants that bear them do. The Japanese with に is used for what I'd render, "Are there yellow flowers having come into bloom in the yard?" Or more commonly, "Are there yellow flowers in bloom in the yard?"
I believe that "blooming" is just the state of existing for flowers. Just like you'd use あります on a person.
This is not a case of using the いる/ある "to exist" verbs. It is a verb conjugation indicating continuous action, and is created using the "て" form of a verb plus いる (or います to be formal). It doesn't matter that the flowers are inanimate because this sentence is talking about what the flowers are doing, not just that they're there.
さく (さきます) = to bloom
さいている (さいています) = to be blooming (continuous action)