In plain-speak: we can have a name tag on the left breast, and an optional squadron patch on the right. While there are brown leather flag patches and platform/crew position patches made, they are not technically authorized.
 
Having said that, a lot of aircrew have them anyway… mine’s got a world map and blood chit sewn into the interior, and a small state flag sewn under the back of the collar. All technically unauthorized… but all of us who have deployed to Turkey have them customized.

@totallynotabronyfim
 
(2) Brown Leather Jacket. Naval aviators, pilots, flight officers, undergraduate pilots, NFOs, and flight surgeons, aerospace experimental psychologists, and aerospace physiologists may wear the leather flight jacket with flight suits, Service Khaki and Navy Blue Coveralls. Eligible enlisted air crewmen, E7-E9, are authorized to wear the leather flight jacket with flight suits, Service Khaki and Navy Blue Coveralls. Eligible enlisted aircrewmen E6 and below are authorized to wear the leather flight jacket with flight suits, Service Uniform (SU), and Navy Blue Coveralls. Only direct point to point transit is appropriate when the flight jacket is worn to and from work with working uniforms (excluding Navy Blue Coveralls, which may be worn in immediate working spaces only). Close zipper at least 3/4 of the way when worn. Management and control of leather flight jackets are outlined in <OPNAVINST 10126.4 series>.
 
(a) Brown Jacket Insignia/Patches. Insignia/patches shall be worn on brown leather flight jackets as follows:
 
(1) Attachments. Logos may be affixed either hook and pile or directly to the jacket. Hook and pile fasteners will be black or brown and cut to the shape of the logo to be affixed.
 
(2) Left Breast. Black or brown 2 inches by 4 inches leather name tag. Centered in the top field will be the aircrew designation insignia (i.e., pilot, NFO aircrew EAWS, etc.). The name in block letters will occupy the lower field and will include a minimum first name or initial and last name. Where appropriate, billet title (i.e., CO, XO, CAG, etc.) is optional.
 
(3) Optional Logos. One command patch may be worn over the right breast pocket. Maximum width may not exceed 4-1/2 inches. No other patches are authorized.

@SH60AWS  
Please explain.

That flag is unauthorized, lol…