@Joy Jones - It seems possible but I think the fees and taxes will outweigh the benefits.
FHA has specific rules about "Identity of Interest" non-arms length transactions. In these cases, it looks like you pay all the normal FHA costs but can only qualify for 85% of the appraised value. (Source: https://www.fha.com/fha_article?id=451 <- not a government site)
You will have to pay roughly 15% Self Employment tax on your flipping if you're using a pass-through LLC taxation method, in addition to State and Federal income tax, on the profit. (Buy at 100k, put in 50k, appraise at 200k, sell to yourself at 200k, get an 85% loan of ~$170k, pay double settlement/closing fees.). You'll pay 'LLC' taxes on 50k, likely least $10k.
Depending on the home's value, closing multiple times (are you buying title insurance again?) might be too expensive. Additionally, if you sell to yourself at a higher price, you're not going to be taking advantage of your 250k 'free' capital gains until it appreciates even more.
That is, if you buy it with your cash as yourself for $100k, fix it up for 50k, wait 6 months, get it appraised for 200k and then get an 80% loan of that amount, you get $160k back in your pocket (minus any fees). Then, if you sell 2+ years later, at $250k, you get the $250k-150k = $100k capital gain tax free.
You can also use a FHA 203K modernization loan to borrow $$ above the purchase price with contractor plans. https://portal.hud.gov/hudportal/HUD?src=/program_offices/housing/sfh/203k/203k--df