I'm in the process of considering a HELoC to purchase my 1st flip, but depending on what he's talking about, I may invest the money in performing notes!  

Does your primary have enough equity for a HELOC?

As an owner occupant you can get access to super low money down financing that let you buy a house with relatively little money out of pocket.And better still is that you can then turn around and get a heloc on that house (ONLY if its your primary residence though) at up to 90% LTV. 

You are going to get a lot of different opinions on this subject, so i'll just give you what I would do:11% is expensive $$$$ and the market is at a high right now, so I would use the ARV of that property and do a HELOC, pull out the equity, pay off the hard $$ lender, and now you are reducing that particular interest to prime + 1 on most HELOC's.  

To Heloc, cash out refi, or 1031.

I actually have two long standing violations: my firewood rack is visible from the street and I have an unpermitted covered, screened deck (something else the ex burned up our HELOC on).

Find a bank that does good business with you, and deposit it or put it to work in low risk stocks, then leverage against the value with the banks money.If your making good deals, you will keep your cash and get 100% financing with closing cost and a 90 day rollover HELOC for rehab.

A HELOC would be my only current source for enough cash to get back into purchasing real estate properly.My question is, how can I convince my brother to let me use at least some of the property equity without taking any type of a legal route.

Why not take a loan of 30-40k HELOC?

I operate my entire business through a HELOC having the ability to have I think 10 separate accounts within it.