At least two birds were flying

Some bird is such that (it was flying and some bird other than it was also flying)

(∃x: Bx) (Fx ∧ some bird other than x was flying)

(∃x: Bx) (Fx ∧ (∃y: By ∧ ¬ y = x) Fy)

or
(∃x: Bx) (∃y: By ∧ ¬ y = x) (Fx ∧ Fy)

Some bird is such that
some bird other than it is such that
(both of them were flying)

or
(∃x: Bx) (∃y: By) (¬ y = x ∧ (Fx ∧ Fy))

Some pair of birds is such that
(they are different
and both of them were flying)

or
∃x ∃y (¬ y = x ∧ (Bx ∧ By) ∧ (Fx ∧ Fy))

Some pair of things is such that
(they are different
and both are birds
and both were flying)