Ever since getting financed for this loan, I have been bombarded with VA offers to refinance my loan, or get a debt consolidation loan etc.

Can I Cash-Out Refinance on a duplex I used a hard money construction loan on?

I'd just sell (or refinance out) of the original one to keep my entitlement intact.

My brother and I will be renovating the property we live in so that after living there for a year we have the freedom to sell the property, refinance and use that equity for a down payment in a different market we're interested in, or rent it out if its able to cash flow.

Once they are stabilized, he refinances at 75% LTV to pay back the investors and have extra capital for the next deal. 

Ideally re-finance out to no less than 1 DSCR, but ideally 1.25 for income purposes to show on DTI, tax returns, etc.

What other changes could I make to possibly refine the monthly payment.

However, county loan limits still apply to Veterans who have previously used, and not restored, their VA home loan entitlement to purchase, refinance, or construct a home above $144,000.Your entitlement can only be restored when the property is sold, or the loan is paid-in-full.

Currently rehabbing but need to refinance soon.

Of course, you could invest using cash only but then you might as well do that overseas and make significantly more money.Many are still pinning their hopes on the fact that they can buy today and refinance later at lower interest rates and hope that these rates go back to sub 3% again.