However, we're well aware that no traditional lender will be likely to approve us for a second mortgage so soon after acquiring our first one since it would make our debt-to-income ratio go through the roof.

Does this mean since the debt was discharged, or since the bankruptcy is removed from your credit report?

I realize I will have to pay gains on it if I don’t do a 1031 exchange in so much time, but I thought if I do flips, we have to always churn the money anyway so why not pay the gains and pay down debt quickly?

Or it could double like this random house in my city did since it's 2006 sale price:https://www.redfin.com/WA/Kirkland/134-8th-Ave-980...So you have to decide if taking on the debt is worth the potential reward, including your specific scenario limitations. 

They did tell me that the auction won't be for at least 6 months and the property can be reclaimed up until the date of the auction if the back taxes are paid off.I've already tasked the owner with contacting the law firm and sending me an email with a breakdown of what's owed (I assume along with taxes owed, there are also some fees from the law firm, just not how much to expect)  After I get this, I'll be able to decide if it's gonna be a worthwhile investment.Assuming I decide to pursue the deal, how should I execute it so that I can finance the owner to pay off their debt without the risk of them taking my money, reclaiming the property, and then deciding not to sell it to me. 

I’ve enjoyed rentals but thinking may be good time get rid of my HELOC debt while prices have gone up a lot.

For example is your 4-plex payment is $1k and you are getting more than that in rent the $1k payment could be zero debt. 

Also the rates are usually adjustable and term shorter than a 30YF.Refi possible advantage if you favor + cash flow rather than being debt free sooner, depends on your equity and amount you're looking to pull out, you might be able to take out the cash you need and still end up with a lower pmt than currently because you're re-upping for a new 30 years. 

Shoot me a DM and I can help connect you with SFR/commercial, agency debt.

If the numbers work and you have sound exit strategies for the deals you analyze you will be fine. 100% agree with @Michael Ablan in that you likely wont make much on appreciation but you can easily cashflow and gain equity through debt paydown.Closing on a Triplex in the area here in a few weeks.