I've been working with a realtor to find flips, but have been unsuccessful at closing a deal due to the steep competition.

I've reached out to a couple realtors, and am already pre-approved for SFH & multi-family purchases (through FHA). 

My realtor states that this is a good deal, however, the numbers don't add up.

My realtor told me the market value of the property would be in the range of $290 to 310K.

Have you tried asking local realtors to put you in contact with some a mortgage broker who could assist in qualifying you for a FHA loan? 

I have an awesome VA specialized loan writer and realtor if you are wanting to bounce ideas off of them.

As @Jeremy Taggart implies, if you have only lived there a year you will be stuck with Capital Gains (GC) tax which along with realtor fees would use a lot of your appreciation. 

I am also a Realtor! 

Realtor.

Depending on if you want to be a realtor and conduct the transaction-portion of the deals, or rather specialize in other parts of the business, be sure to be specific in where you want to be great and talk to those people doing that line of work.I personally had my license and let it lapse since I instead would rather pay an agent to handle the transaction on my behalf while I look for investors and individuals wanting to partner with me on deals.