Battle Familiar

Can a Medium size familiar such as a zombie that has Battle Familiar cast on it with the "Flyer Form" act as a flying mount if my character is Small sized?

The normal stat block for Zombie (found in appendix B of the PHB) is a CR 1/4.  This means the CR is too high.  The stat block for the Battle Familiar changes the CR to "None" which was weird enough to make wonder. 

I suspect the answer is "No" but I think it would be funny to have a flying zombie haul me around a battlefield.  I guess even worse is that if I use a Deer as a familiar I can no longer ride it if I cast Battle Familiar on it as it would have it's stat box changed as well.

I don't have the details of Battle Familiar, but a Warlock with Investment of the Chain Master can have a Skeleton and infuse it with a Fly Speed, so technically is possible.

Now... there is an additional requirement: "You can control a mount only if it has been trained to accept a rider." (EDIT: I'd allow it as DM)

The thread Wee Skirmisher: RAW or RAI? was about it.

EDIT: add tooltip.

FYI it is important to distinguish using a creature as a "mount" - which generally requires them to be approximately horse-shaped and specific riding equipment for you to sit on/in to be appropriately mounted on them, vs a creature grappling you and carrying you around - which any creature can do as long as it has some way of holding onto you. 

It can function as amount, but the most restrictive caveat is carry capacity.  As for the RAW requirements, willingness, size restriction larger than you and finally anatomy that can handle your position of carry (broad back of horse, large shell giant turtle, princess carry in arms humanoid). Note the skeleton cant swing a sword or shoot a bow if youre in a princess carry.

150lb at Str 10 without the spell, for 1 minute with a spell its 240lb.  Your weight, your gears weight and your familiars weight of gear must not exceed this or it's speed is dropping to 5'  Pray you dont enter a zone with speed reduction or its hit with a Slow causing bow arrow at that point.

Worth noting, you can just make anything fly with investiture of the chain master invocation too instead of the battle familiar spell if you have 5 levels of warlock, but it doesn't get hover.

For a permanent flying familiar mount, use chain master and live with 150lb weight limit.  For a temporary mid fight only use battle familiar for its greater stats...

Or you know... use a giant fly as anything which can summon a familiar since its a CR zero large beast and can carry medium or small people, has a reasonable 19 HP and a 60' fly speed.  Also it can carry 210lb base doubled to 420 due to being large sized, and you can always use battle familiar to buff its HP with temp HP.

I also recommend Familiar Friend origin feat in Arcana Unleashed.  It adds base HP to your familiar equal to two times your character level and being invocation free you can do this with any class, as it grants the find familiar spell.  There's a follow up feat of Warlike Familiar that grants the Battle Familiar spell requiring L4+ and not requiring spellcaster.

Oh and your main issue with any of these plans is the terrible HP and AC of a familiar.  for combat mount battle familiar spell is heavily recommended, and even that wont keep it alive.  Fireball is your enemy.  I think the best option is battle familiar buffed giant fly, with familiar friend origin feat.  Chain master is a big bonus especially since you could use the brute form as chain master invocation grants flight (and now you can use your bonus action to make it multi attack on your turn).  Fly's higher strength means when the spell ends from loss of temp HP, it can still carry a reasonable amount plus your not locked to small races.

Important to note: imps, skeletons, sprites? they all lose their stat blocks while battle familiar is active.  Skeletons are no longer proficient in armour, and can't use swords or bows, imps have no invisibility or poison sting, sprites have no armour proficiency, bows, swords, invisibility, or alignment senses... 

They regain them when they loose the Battle familiar spell.

Personally, I'm ruling that only the size is relevant to determining whether your movement is affected when grappling, not the creature's weight.

Movable. The grappler can drag or carry you when it moves, but every foot of movement costs it 1 extra foot unless you are Tiny or two or more sizes smaller than it.

Regarding a Giant Fly as familiar, it's not clear, so IMO, it's an "ask your DM" case:

- Types of familiars
- Find Familiar: Giant Fly
- https://www.dndbeyond.com/forums/dungeons-dragons-discussion/rules-game-mechanics/245072-error-report-magic-item-reference-cards-common-and?comment=5

"Mounted Combat: A willing creature that is at least one size larger than a rider and that has an appropriate anatomy can serve as a mount"

Now, the Battle Familiar spell changes the shape of your familiar, because its a statblock replacement.  The flying form presumably has wings.  It does not matter that your familiar was originally a zombie.  I would generally presume a Battle Familiar has appropriate anatomy if you wish it to, its your spell shaping the creature.

Flying creatures generally require an exotic saddle to actually mount.

Seems completely legit to me, so long as you have the saddle.

Note, what 'appropriate anatomy' means is unclear, since not everything that is canonically a mount is horse-shaped.  Even in the real world, it would be hard to maintain that an elephant is actually horse-shaped.  I would generally understand an exotic saddle to be designed specifically for the mount its going on, and that means 'appropriate anatomy' really just means 'you have an exotic saddle for that creature'.  So you could use your zombie as a mount if you had an appropriate 'saddle' designed for it.  (Think Yoda riding Luke's back during the Dagobah training).

As far as controlling your mount, your familiar is in constant telepathic contact with you, capable of understanding you, and your companion.  It should be cooperative and easily directed.  I would always treat it as a controlled mount, no matter what form it was in.