From reading the rules, it appears that level 6 Circle of the Moon druids should be able to wild shape into a flying beast.
Many sites on the internet suggest that they cannot.
- https://www.dndbeyond.com/classes/druid#CircleoftheMoon
- https://blackcitadelrpg.com/circle-of-the-moon-druid-5e-guide/
- https://www.hipstersanddragons.com/circle-of-the-moon-druid-wild-shape/
- https://www.dndbeyond.com/posts/635-druid-101-wild-shape-guide
From reading the rules (which are at the end of this post), every time for non-moon druids at 2 and 4, it calls out non-flying. For moon druids at level 2, it says must check Wild Shape or Beast Shape table.
However, for Moon druids at level 6, no such disclaimer exists. Every other location speaking of CR limits includes fly/swim limits but not here. Does that mean Level 6 Moon Druids can wild shape into flying beasts?
Rules as Written for wild shape for non-Circle of the Moon druids:
Wild Shape Starting at 2nd level, you can use your action to magically assume the shape of a beast that you have seen before. You can use this feature twice. You regain expended uses when you finish a short or long rest.
Your druid level determines the beasts you can transform into, as shown in the Beast Shapes table. At 2nd level, for example, you can transform into any beast that has a challenge rating of 1/4 or lower that doesn’t have a flying or swimming speed.
... table showing that level 8 can fly (with an example of Giant eagle)
Wild Shape Improvement At 4th level, you can use your action to magically assume the shape of a beast that you have seen before of challenge rating 1/2 or lower that doesn't have a flying speed. You can use this feature twice. You regain expended uses when you finish a short or long rest.
Wild Shape Improvement At 8th level, you can use your action to magically assume the shape of a beast that you have seen before of challenge rating 1 or lower. You can use this feature twice. You regain expended uses when you finish a short or long rest.
Circle of the Moon Rules as Written:
Circle Forms The rites of your circle grant you the ability to transform into more dangerous animal forms. Starting at 2nd level, you can use your Wild Shape to transform into a beast with a challenge rating as high as 1 (you ignore the Max. CR column of the Beast Shapes table, but must abide by the other limitations there).
Starting at 6th level, you can transform into a beast with a challenge rating as high as your druid level divided by 3, rounded down.
...
Circle Forms The rites of your circle grant you the ability to transform into more dangerous animal forms. Starting at 6th level, you can transform into a beast with a challenge rating as high as your druid level divided by 3, rounded down.
Summary:
DNDBeyond has post suggesting that Moon druids start to get flying at level 8, which seems pretty damning. However the way the rules are written, every other single place CR is listed, it includes flying/swimming restrictions. At level 8 for non-Moon druids, it does not explicitly state they can fly, it just does not say they cannot fly. This is identical for level 6 Moon druids, suggesting they can fly. For other places in the rules, where higher level text does not include verbiage from lower level text, it means the verbiage excluded no longer applies.