I would like to double close a wholesale deal but how could I structure the timeline if I were to market the property on a online public auction? Or how should I go about the closing date on the first contract?
It's best to have your buyer lined up first so you know for sure that you're going to get the deal already sold vs piss off the seller if you had to back out because you never planned on buying it yourself.
Until you know the market really well, I wouldn't just put a property under contract then attempt at or assume someone will pay more than you got the AB side under contract for until you know the market or know your buyers and what they will pay at minimum.
If you want to try and get top dollar, get private funds, but the deal then as soon as you buy it, list it on the MLS. That will be the BEST place for you to get top dollar for the property without an auction.
You can still share other buyers offers with everyone who submit offers if you'd like to see if anyone will amend their existing offer later if you think you have a strong enough property in higher demand.