Not without larger changes.
A RAW interpretation of the UA Beast Ranger says no, there are no flying animals in the list of creatures, so adding a fly speed would not fit the pattern.
However, for the purpose of trying to say yes to player requests for options (AKA, with DM approval), here is my analysis of the Owl/Giant Owl stat blocks as ranger companions.
The Flyby ability of the Owl and Giant Owl are significantly more powerful for a combat proficient creature than anything else available for UA animal companions. Combining this with a flyspeed of 60ft, and they could fly in, attack, and fly out without taking an attack. This effectively makes them untouchable by melee combatants.
This feature is also not comparable to the abilities of other animal companions such as: Keen Smell, Charge, Relentless, Sure-footed, and Pack Tactics.
Also, the other animal companions have a 40ft walking speed, and do not have darkvision.
All in all, this companion is objectively better than the other UA companion options. 120ft darkvision, 60ft fly speed, and the flyby ability are all individually more powerful than the standard companion.
I would start by removing/reducing all of these features. Limit the darkvision to 60ft, reduce the flyspeed to 40ft, and eliminate the flyby ability. Then reduce it to fit the UA rules on companions. Do not replace flyby with a new ability, since you still have some darkvision and a fly speed.
Remember, the UA Beast Ranger is a bit OP compared to the other ranger archetypes, with an effective multi-attack at level 3, plus a pseudo-multiattack on top of this at level 5, so you should err on the side of underpowered when creating a new ranger companion option.