Does anyone know if there's any DA forms or other documentation needed to give to my chain of command if I wanted to get a civilian job?

What you're asking about is called "Moonlighting". There are various rules, laws, ethics, and policies that effect what you can do while moonlighting. There are a whole lot of rules about what you can do if it's your own business, a lot less if you're just an employee at another business. The most important rule for you is that your Commander must agree to allow you to moonlight. If you don't receive approval from your Commander for your job, even if it's delivering pizzas, you can be punished. Even if you have your commanders approval you can still be punished if you break one of the rules. Most of them deal with making money from Soldiers, selling on post or to the army, or jobs that would embarrass the Army.

With all those warnings though, lots of people still have side hustles. When I was younger I would throw boxes at UPS around Christmas for extra cash. 10/10 do not recommend, that's hard work. But other people work as personal fitness trainers, scrap metal collectors, real estate flippers, eBay resellers, Amazon delivery, Uber eats delivery, Lyft drivers, and landscaping. Just make sure your second job never interferes with your Army job, make sure your command is aware, and don't pick any job that could discredit the Army or make it look bad, ie don't start an OnlyFans account, become a stripper, or work at a Marijuana dispensary.

What has not been brought up that a prospective commander might consider is the “WHY.”

If you want to make more money for the sake of more money, by all means, motive is irrelevant if you can do it without conflicting with your Army obligations. More money for savings, more money for material consumption, more money to save a nest egg for your transition, whatever………. all rational reasons.

What a commander might be concerned about is you’re in a hole and potentially digging yourself deeper into it, and potentially not going down a path that will result in success and continue to over extend yourself further leading to future failure and strife.

The WHY isn’t for discussion here, that’s for your chain of command. I would certainly ask it, and you could easily blow me off with any of the above for mentioned reasons that wouldn’t cause me Red Flags. I’d only ask them to cover my end of leadership responsibility.

Is a trip to Financial Counseling necessary? That would be part of my counseling statement: Verbiage to the effect the motivation is not credit problem induced.

I’m of the opinion the US military pays pretty well for those who are even just reasonably responsible with their finances. It is also the only employer to pay us MORE for the sake of being married or having dependents. As well, a large portion of what we earn (BAH for example) is TAX EXEMPT, making the take home effect of our pay checks on par with the civilian equivalent that has a higher income.

So “WHY” might leave a commander wondering. Maybe I'm just overly critical given my civilian profession.

Just do a memo for your commander acknowledging your intent to moonlight. The outside employment rules are really focused on people who work with contractors in their offical capacity but the military tends to apply the rules to everyone for some reason.