No - They do not fly in the Firmament/Vault of heaven
Well, the Hebrew language is so ambiguous that no precise translation is possible. The word "al" can have all these meanings:
about (27), about* (1), above (43), above* (16), accordance (2), accordance* (1), according (40), according* (2), account (11), account* (2), across* (1), addition (4), addition* (1), afflicted (1), after (14), after* (1), against (536), against* (1), along (11), alongside* (1), although (1), among (7), around (11), attention* (1), because (82), because* (49), before (10), before* (19), behalf (18), behind* (2), beside (47), beside* (6), besides (5), besiege* (1), besieged* (13), besieging (1), besieging* (5), better than (1), between (1), beyond (3), beyond* (1), bordered* (1), care (1), carried (1), charge (31), charge* (1), command (1), committed (1), concerning (97), concerning* (5), confront (1), confront* (1), connection (1), conquer* (1), consider* (3), considered* (2), contrary (1), corresponding (2), corresponding* (1), crowns (1), defiance* (1), despite (1), due (1), duty (1), east* (7), encouragingly* (2), engaged (1), even (1), everywhere* (1), faces* (1), facing* (1), far (2), forsaking* (1), full* (1), fully* (1), have charge (1), inasmuch* (5), instead* (1), leave* (1), length* (1), more than (2), much (1), named* (1), near (4), next (9), next* (13), now* (1), obliging* (1), off (6), off* (5), opposed (1), opposite (1), opposite* (4), ornamented* (1), over (538), over* (6), overflowing* (1), overflows* (1), overlooks* (3), part (1), planned* (1), pleased* (1), pleases* (2), presence (2), pressed* (1), prompts* (1), reason (2), reason* (6), received (1), regard (3), regarding (1), respect (1), responsibility (1), ruthlessly* (1), sake (4), sake* (1), sakes (2), settled* (1), since* (1), so (1), so* (2), sorrow (1), spite (2), steward* (4), surround* (1), sworn* (1), task (1), than (1), than were over (1), theirs* (1), therefore* (139), thereon (1), through (3), throughout (3), together (3), too (3), top (1), top* (2), toward (20), toward* (5), under (12), until (1), upright* (2), upside* (1), urged* (1), view (1), way (1), when (1), where (1), where* (5), wherever* (2), while (1), why* (10), within (13), within* (1), wore (1).
Birds were supposed to fly above the firmament, against it, behind it, across it, facing it, around it, even in it, beyond it, over it, beside it... who knows.
The most frequent usage of the word is "above it".