How to sell current home to purchase house hack invesment

[Alexander Ball]

As the subject states, I have a dilemma that I am having a hard time navigating myself. I now own a SFH that is my primary residence, the first property I have ever bought, and I have owned it for about 30 months. My Realtor suggest that it comps at 22k-32k what I paid for it after improvements I've made. Essentially, I am looking at walking away with 15-25k after sale, enough for an FHA 203k loan down payment, closing costs, and reserves.

My frustration comes from my inability to figure out how best to proceed.  I can't just sell the house and be homeless while house shopping.  I have a bully breed type dog that will make renting very prohibitive, especially if I need a month to month lease.  I'd be moving and then moving again soon after.  

There is a house I am eyeing that is on the MLS, a couple guys basically part way through flipping, and a duplex that I can get for a 100k loan with repairs included that rents at $1500 to $1600. It cashflows at 100 conservatively and there is room to add value.

Do I make an offer contingent to the sale of my primary residence?  Why would they want to stay in contract with me while I wait to close?

Should I just move out, eat the costs of finding a place to live month to month?  That doesn't seem like the way to go.

I feel stuck.  I know there is a way to figure this out, I am sure there are many that have had their investments tangled up somehow in their primary residence.  Please help.