To quickly evaluate a a deal where there is no asking price, I usually look at capex required, adjust the property taxes (based on comparable sales) and perhaps play around with the vacancy and reserves.Is there anything I am missing?

The bank as been listed as the owner for a couple of years now on some while others where listed as the owner within the last six months to a year but not listed for sale. 

You may even contract on your new property before the closing of your sale. 

But, until I started talking to them, all they knew was they wanted to sell, but they hadn't yet prepared a single thing for the sale.

Your family member could also provide the financing on it and make money every month with a positive cash flow spread between the debt and the rent collected or be like a guarantee person that is the main backer for the long term loan your Bank or other lender that  owns that property with a long term loan with that property  on a security  loan until that loan is paid off.Not saying the fix up budget makes this decision fairly difficult but i would say to not have a house that needs over $5,000 on the "make ready" expense to make a 20% gross return giving a cost price and sales price you gave on your example.What you could do to find a deal is pretty limitless. 

Without proper financials or there is no basis for valuing the sales price, the whole reason for an inspection period is to uncover uncertainties.

Offer properties for sale with fake rehab numbers. 

This is one of the most expensive parts of town so I was thinking this could potentially be a very profitable flip even though it is not currently listed for sale.

Prefabs for Chicago will be approved and ready for sale in 6 mo.

Go look at properties for sale with a realtor bring along a carpenter or contractor with you ( buy them lunch) bring a tablet and write down the issues and costs as they rattle them off .