Uncle is currently in VA hospital diagnosed with dementia and unable to live on his own. They asked if I'll be proxy. What do I need to do?

Sounds as if they are not being clear in explaining the different terms to you. "Proxy" is usually the power to make health care decisions and sign related paperwork. "Guardianship" is control over the person and the person's property. This allows you to make decisions about everything on his behalf, using his funds/resources.
Ask them to send you the proxy form so you can read it.
I'd try hard to connect with the assigned social worker to see what the VA has in mind once he is medically stable (may already have reached that status, so needs to move out of an acute care medical bed.).
Getting him to your area for nursing home placement will be harder than getting the VA to place him in a nursing home where he (and they) are located.
The VA can petition the court to request an assigned guardian for him - but it is easier for everyone else if YOU agree to take on that role.

I think its just to have someone to make Medical decisions. As said, it does not make you responsible financially. Since he has Dementia, you cannot get Power of Attorney because he has to be competent to assign you. If you don't mind making medical decisions then ask the SW what is needed to become a proxy. If you r not comfortable having this responsibility, then say no. The State will have to appt a gaurdian who will make these decisions for him.

With guardianship you will need to go to court with proof of Uncles incompetence. The State will require you to report to them yearly concerning Uncles finances and health. For the cost, I personally would not do it.

Your Uncle should have assigned a POA long ago. He should have had a Living will saying what he wants done when he started having health problems.

Looked on Medicare.gov concerning Medicare Plus. They are Medicare advantage Plans and Medigap. Medicare Advantage plans are plans that Medicare has contradicted out. Suppose to get the same advantages of Medicare but they are HMOs/ PPOs so you need to stay in their Network when it comes to providers. Straight Medicare you can go to any provider who takes Medicare. Not sure why he would have a MA and not straight Medicare if going to the VA. Vets I know use the VA as their secondary insurance.

Is Uncle living in another state? If so this will make it hard to deal with his doctors.

Ate they asking you to become his health proxy, meaning that you will be asked to make medical decisions only? Or are they asking you to get guardianship?

I woukd clarify with the VA social worker what is being asked of you.

Do not sign ANY forms indicating "responsible party" with your own name.