If I can accomplish it for $30k-40k it would be a good investment for me, but I know nothing of what's feasible or not. 

@Rickey Stevens check this pdf download called "The Top 20 Real Estate Books Every Investor Should Read" at https://www.biggerpockets.com/books

I am guessing I would need to form an LLC in TN for that property?

I think you could use the second tab to set out a bid form for your GCs.

As this is a risk for me to tie up a chance of not selling to anyone for possibly 3 years, is it possible to "tie it up" for them, but say something like "price to be determined by appraisal at end of lease, with a minimum of $215,000" is this legal, or common?

Finally, if that fails you may see what the banks offer as far as low down-payment conventional home loans, I know when I was looking earlier in the year (June-July) there was an option for me to do conventional at 5% down payment.

That's a little pricey for me but if it's the best for the money I will take it.

Since her home was flooded due to an interal plumbing issue and the insurance company is paying to remodel the existing old (1920s) and dilapidated structure (could tell by looking at some of the 2x4 studs revealed in the partial internal demolition), I decided to find out if my mother can use the money should would receive from the insurance company in the form of a check, put that towards the remodel, and in addition secure a construction-to-permanent loan in order to fund the complete transformation of her 1 bed 1 bath 1,200 sqft home into a 2-story duplex that she can rent out, airbnb, etc.

what forms do you have your contractor sign before starting a flip? 

Not sure if it is incorrect but it worked for me.