added value with elbow grease through painting, functional updates, laying a brick patio, and light fixtures.

The house itself is considered inventory and the profit is treated as ordinary income, which will be passed through to you and reported on your personal return via W-2 wages and the K-1 from the S Corp.The wages and profits are taxed accordingly.

I feel like this isn’t correct since it’s taxed as ordinary income right?

Rehab the property before placing first tenant(s).Move in/ move out inspections and bi-annual inspections noted in the lease agreement.Install 1/4-turn angle stop valves at all sinks and toilets.Install new faucets.Replace backyard decks with a patio slab and step at sliding door (if needed).Do not install screen doors.

Yes, the deprecation might offset the profit (Ordinary income) from the flips if you qualify as REPS and you have materially participated in your rentals. 

You are taking the depreciation, but your adjusted income phases out the ability to deduct the loss against ordinary income.

Taxed at ordinary income if you lived there for less than 1 year. 

First, there are no capital gains on a flip, it is ordinary income.

Each unit also has its own patio and small fenced yard.

https://www.irs.gov/publications/p544"Depreciation RecaptureIf you dispose of depreciable or amortizable property at a gain, you may have to treat all or part of the gain (even if otherwise nontaxable) as ordinary income."