Should all branches of the military wear a US flag on their uniform?

Works for the Army... but not sure that the other Branches do and why.

Whether your are wearing work, combat or dress uniform would not matter since when any uniform is soiled/stained permanently or if it were to become torn then the uniform needs repaired, replaced or retired. The argument of not affixing the US Flag for this reason is rubbish in my opinion. I also feel that all branches of the service as well as their auxiliaries should be displaying the US flag on their uniforms and I am also of the opinion that the US Flag should be permanently affixed to all uniforms and not be affixed in a fashion where the can be easily removed such as velcro.

Remove the reverse field, put in on the right way and make it part of the work uniform, or remove it all together.

I'm indifferent, but I will point out to you that the Army is NOT the only branch that wears the flag. Aircrew in AMC also wear the flag on the left shoulder. There are probably some other examples as well (any Navy folks want to chime in?), but I'm in ACC, where we have the wing patch on the left shoulder.

Downrange yes - Garrison no

I think it should be worn on uniforms.

Hopefully I can provide some insight on this. I happen to do oversight for said organization for my reserve job. I am ina CAT-E PIRR position called CAP-RAPO or Reserve Assistance Program Officer for CAP-USAF which is the congressional mandated Air Force oversight arm for CAP.

Back in 2007 CAP had a very pretentious National Commander by the name of Anthony Peneda. He promoted himself to a (CAP) Major General. When previously that position was only authorized Brigadier Gen (CAP). He was hell bent on trying to make the organization look more like the real Air Force. CAP officers wear a distinctive modified version of the AF uniform by wearing Grey Epaulets both the Service Dress and Light Blue Shirt as well as having a distinctive hat device versus metal grade on the flight cap. On their BDU's they wear ultra marine blue name tapes and insignia's as to not be confused with an actual AF Officer.

Peneda did some changes like adding "US Civil Air Patrol" to the blue name tape instead of just Civil Air Patrol, which it has reverted back. He also invented a new CAP uniform that almost bridged our service dress. I will admit it actually looked more legit than ours ironically. He had a new Double Breasted Coat made where now they could finally wear those prized metal insignia on their shoulders versus the Grey Epaulets. They wore a white under shirt instead of a blue one, but now wore the AF regulation Blue Epaulets. The only thing that made it not appear to look like an AF uniform was that prior/current military serving in the program were not allowed to wear any federal military ribbons or devices. However if they were on base being that most of us rarely wear our service dress any way I could see people salutes to CAP Senior Members. That caused some contention with the USAF because since it was not on the official AF uniform we could not tell them no.
The flag was also the addition to the BDU to make it appear more military like. Since then Maj General (CAP) Peneda was 2B'd from the organization for cheating on an Air Command and Staff College (ACSC) test. Once the new leadership took over they decided to try clean house and their reputation by reverting back to the status quo.

I don't have a problem wearing the US flag on the BDU since they can wear it on their flight suits.

My overall opinion of the organization is this. Having graded two Opevals and directing 1. They are very professional at what they do when running incident command centers, executing SAR/DR missions from AFPRC or the state that they are in. However, every now and then I run into a goob who speaks to me as if I am subordinate to him. Not disrespectfully but just in a tone that sounds like he is talking to a subordinate officer. I had to correct a CAP member who called my assistant who happens to be a Reserve Senior Master Sergeant as Sergeant. I had to explain that SMSgt's are not called sergeants they are Seniors or Senior Master Sergeants. In the CAP-RAPO program we are unique in the sense that anyone from an E-5 to a Reserve O6 can be a CAP-RAPO. To the Cap personnel the oversight authority of any CAP-RAPO is the same no matter what grade they hold.

It drives me nuts every time I hear a CAP person bitch that they should be allowed to look like the real AF personnel. CAP should be proud at what they do but they should understand that wearing the USAF uniform is a privilege and not a right. A 2LT in CAP does not go through any officer accessions course unless they are an actual military officer. All that is required for 2Lt(CAP) is completion of the CCPT and SML1 training and wait 6 months.

Sorry for the tirade it drives off the wall when the very small few in that organization think they actual officers.

You're missing an option there SSgt (Join to see);

"Army should wear the flag. Don't care what anyone else does"

While I understand the respect for the flag, the one on the uniform is NOT the flag that falls under the U.S. Flag Code. It is to be considered a flag printed article of clothing and acted upon as such. Allowing the patch to touch the ground or get dirty/greasy is not the same as letting the flag itself touch the ground; the patch is not even to federal standards for official flag dimensions, if my memory serves me correctly. Military forces across the globe wear their flags on their shoulders, and there is no reason we should not be doing the same.

Not on your day top day clothes, it cause to much chance of damage to the flag, which should be avoided.