Is it a magic item?
Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?
Is it a spell attack?
Is it fueled by the use of spell slots?
Does its description say it’s magical?
In order then we have:
No. No. No. No. No. No.
The ability to fly is not itself a spell even though we only have that ability because of a spell. This is similar to cases made in the following questions:
To quote to top-voted answer from each one of them:
A polymorphed beast has the stats of whatever it has been changed into. Unless the creature it is transformed into has some ability that makes their attacks magical, the creature's attacks are not inherently magical. [...]
[...] The key to knowing if a creature's attacks (physical and ranged) are considered magical is some feature in the stat block says they are.
While it's not specifically stated that they aren't magical, it is clear that they aren't due to the class feature of the Circle of the Moon Druid at level 6 [...]
[...] The summoning is the magic, not what the summon does later. Otherwise, characters could summon rats, tie it to a stick and declare it a +1 rat flail. [...]
[...] In contrast, if you look at say the planetar, it specifically says "the planetar's weapon attacks are magical."
[...] Walking or flying are mundane movement, even if it was magic that gave you a fly speed or changed your physical size. [...]
Even if the rules aren't entirely clear here (after all, the checklist is from the Sage Advice Compendium document and not the rulebooks themselves), it is rather clear where people stand (well... at least just people who vote on TTRPG Stack Exchange which I cannot know how representative that sample is of the general populace or of general players of TTRPGs).
If you want to say that a fly speed granted by polymorphing into a creature is a magical fly speed, you would also have to say that an attack granted by polymorphing into a creature is a magical attack (at least, to me you would, as those are structured near-identically). This is certainly something you could do as a GM, but be careful of the ramifications (such as leaving forcecage becoming easier than even the easiest of pies... or cakes, if those are your preferred baked good for use in similes about ease).
1 Thomas Markov not included