FTHB Question - Is an FHA quick flip a good idea?

[Isaac Bell]

Rookie question here: 

I'm an FHA FTHB in Austin looking at buying the SFH where I rent (for $1650/mnth) in an off-market sale. 2-floor 3/2.5 home in the 78744 area code, but schools in the area have bad ratings. Sale price is $300K, and the seller estimates 5K needed in repairs.

My lender estimates $2k/mnth on total mortgage payments, which gives me negative cashflow of ~$400ish/mnth if I keep the same rent. Ideally I plan to hold the property for a month or two, and sell after minor repairs are done. With the bidding war currently going on here, I'm hoping to sell in the $315K-320K range pretty easily. I plan on asking the seller about paying closing costs /repairs, and rolling that into the loan price.

Online calculators say that I'd get $1,500 capital gains tax on a $10K profit, which isn't too bad for a 1-3 month investment.

How good or bad of an idea is this? Are there details I'm missing? Can I not sell immediately on an FHA? I only have the means to do this once, and I'm nervous. Any advice is appreciated.