Palmetto bugs can fly, just not very good at it.
Can a Palmetto Bug Fly? Florida Flying Cockroaches | APB

Fight grocery inflation!!

Fry it with some teriyaki sauce. Tastes just like chicken

Negative! What a floridian considers a Palmetto bug is incapable of flight. Too many people from other parts of the US consider anything in Florida a palmetto bug including a moth? Go figure.
You gotta have wings to fly. A palmetto bug is a wingless, segmented roach.
EDIT: This is a Palmetto Bug as we Floridians know them.
Florida woods cockroach - Eurycotis floridana (Walker)

Almost everything about this post is incorrect. Palmetto bugs are cockroaches and can, indeed, fly.

How are Cockroaches and Palmetto Bugs Different? | Orkin

"Almost everything about this post is incorrect. Palmetto bugs are cockroaches and can, indeed, fly."
I'm pretty confident you aren't from Florida. lol

The Orkin site doesn't even show a picture of one. Here, let's use the UF link instead. Technically yes, they have wings but so do penguins... it doesn't mean they can take flight.
Show me the wings please??

Florida woods cockroach - Eurycotis floridana (Walker)

Which is exactly what the link I posted stated, if you took the time to read it.
They have wings, but use them for gliding not taking flight.

I'll leave it at this. For what a Floridian would term as a Palmetto bug. They cannot fly, glide etc. I've seen a few fall from bushes and their glide path was similar to a walnut flying out of a tree. They are ground dwelling bugs incapable of any type of flight but like anything, they fall pretty well.
They cannot fly, they cannot glide. Period!

Florida woods cockroach (aka palmetto bug)

Quote/s from the UF entomology site (they kinda know bugs) :

"but lacks effective flight wings and is slow moving."

"species also lacks developed wings in either sex, instead having reduced wing pads and absent hind wings."

"Figure 3. Vestigial wing formation on an adult Florida woods cockroach"

Vestigial definition:
(of an organ or part of the body) degenerate, rudimentary, or atrophied, having become functionless in the course of evolution.
"the vestigial wings of kiwis are entirely hidden"
Rather like the tail bone we all have. We wont be hanging from trees anytime soon.

If you have a palmetto bug that is capable of gliding, I would suggest you contact the UF's bug people right away. Maybe you'll get to name the new sub species.

From the link @ UF that you provided;

"However, palmettobug may also describe any large cockroach that may frequently be encountered as a peridomestic pest, and has included several members of Eurycotis and Periplaneta (Gurney & Walker 1976) such as the American cockroach, Periplaneta americana (Linnaeus), and the smokybrown cockroach, Periplaneta fuliginosa"

Both of these species are capable of adult flight.

Omg you had me laughing like crazy 😂

This is not a cockroach of any kind. It is a Tersa Sphinx moth 100%.

They look like Hummingbird moths. Harmless to us but maybe not for plants

It looks like a Hummingbird Moth. Harmless to us but, perhaps, not for plants

Educating is like pushing a rope.