How can someone prove that they can wear a combat patch for deploying to Kuwait under OIR and OFS?

If the 82nd wanted you to have a patch, then you would have gotten orders from the unit uoi were with. Normally the Battalion issued orders showing all who were on the them.

I have soldiers with TCS orders stating operation inherent resolve -Kuwait. This means they are not entitled to a patch because they’re in Kuwait. Only those who pushed into Iraq are eligible

The regulatory requirement is AR 670-1 ch 21-18: deploy to a country listed, in support of an operation listed.
The "proof" is an order putting you in that country in support of that operation.

So here is the regulation:
AR 670–1 • 26 January 2021 43
21–18. Shoulder sleeve insignia–military operations in hostile conditions
a. General. Authorization to wear a SSI indicating service during military operations in hostile conditions (MOHC) (formerly known as the SSI-former wartime service) applies only to Soldiers who meet or have met the following criteria:
(1) The Soldier must actively participate in or support military operations in hostile conditions, which must include exposure to the threat of hostile action or fire, either directly or indirectly.
(2) The Soldier’s participation or support described in paragraph 21–18a(1) must occur while the Soldier is located in an area that entitles the Soldier to receive the combat zone tax exclusion and entitles the Soldier to receive Hostile Fire Pay or Imminent Danger Pay (IDP).
(3) A general or flag officer in the chain of command must request DCS, G–1 approval for wear of the SSI–MOHC.

furthermore here are the designated campaigns:
(16) Operation Inherent Resolve: between 15 June 2014 and a date to be determined, for Soldiers deployed to Iraq, Jordan, or Syria in support of OIR, who received combat zone tax exclusion and hostile fire/IDP as identified byUSCENTCOM Command Center–Joint Staff for Personnel and Administration. Soldiers who were deployed in the area of operations on training exercises or in support of operations other than OIR are not authorized the SSI–MOHC, unless those exercises or operations became combat or support missions to OIR.

Notice Kuwait is not an area in this operation.
(17) Operation Freedom’s Sentinel (OFS): between 1 January 2015 and a date to be determined, for Soldiers deployed to Afghanistan, Pakistan, Yemen, and Djibouti in support of OFS who received combat zone tax exclusion and hostile fire/IDP as identified by USCENTCOM or AFRICOM Command Center–Joint Staff for Personnel and Administration. Soldiers who were deployed in the area of operations on training exercises or in support of operations other than OFS are not authorized the SSI–MOHC, unless those exercises or operations became combat or support missions to OFS.

Again notice Kuwait is not in this theater.

You were NOT exposed to hostile fire or imminent threat in Kuwait. Anyone flying into those territories are then subject to hostile fire or imminent threat and are thus authorized the SSI.

If the army says that you can wear ikt, bewcause what you were doing, then wear it.

It is NOT a "combat patch" it is a "Foreign Wartime Service" patch. If your unit deployed in support of wartime operations you may wear the patch. It is entirely irrelevant that some of your unit went forward from Kuwait but you did not, the very same orders authorize you to wear the patch. No commander's memo is needed.

I even had an FSO authorized a patch for an ROTC rotation to Djibouti. Also a bunch of the tenth mountain patches you see out there are for Africa not the ME.

I know it's apples and oranges, and don't know what the Regs are on it. What do you think I thought of the company clerk that wore the PUC on his uniform because our unit got it for the worst one month of combat I saw. He never left base camp during that time BTW. Tell your friends any combat award or patch not honestly earned is stolen valor IMHO.

I'll try to keep it simple... A Combat Patch is only awarded to Company Echelons and below that Do Not Have their own Unit Patch (stated in an ALARACT Message). The Combat Patch is award 30 days after assignment to a Combat Zone and issued by the C2 element. The award letter must be signed by a CG or delegated to a COL and signature cannot be "signed for". I hope this explains it for you.

I am a old Marine and I was wondering why you would want to wear something on your uniform that you know for a fact you did not do So that should told right off Hey this says combat and watching tv in Kuwait doesn't count So you wear it and another soldier sees you and asks where were you at So then you are going to have to justify it to whoever Then work on yourself

Dah! A set of orders stating you were in theater