You can establish a personal LLC and use it to buy a business.

I don't know this person or company from a sack of salt or what  they do..

NOT judging, I am truly curious the mindset's of such persons.

I was drawn to real estate as a way of investing money I have saved up (around $130K with additional funds to leverage out of a 401K if needed), and potentially creating reliable cash flow over the next 10 years. 

They knew all along they weren't going to fund this flip.

Securing funding has been challenging, particularly because my business documents reflect low revenue from only one duplex, and I am currently between jobs.I have identified a reasonably priced piece of land and have saved a small portion of the funds from my duplex sale to invest in this venture.

Really the person that is going into the flipping game should know the market very well to do these comps on their own, and back it up by asking their trusted real estate agent/professional for confirmation.

What is the best lending strategy to fund this new construction?

If I could just ask one more question, i have a separate account with no co mingling of funds.

we can do it not rented but rate will be significantly higher. easier and more cost effective to rent it. unless the bridge money needs to be paid back asap or you need the funds back to buy more, then a cost analysis needs to be done. personally id get it rented at market rent or a touch below if time is a factor.