I would simply add the 2021 improvements to the basis of the house.

and not show part as ST and rest as LT?

'Flips' are ordinary income/loss, not capital gain/loss (short or long term). 

Sale price is revenue.  Cost, including improvements, is cost of goods sold.

I would say it depends on whether or not Flips is a business (ordinary income) or investment (capital gain)

If the person is regularly involved in flipping houses then it is a business. But if they just boght their first house because they think they could make money on it by fixig it up I would say that is an investment.

Regardless, any improvements are added to basis of the home and treated as a single unit for CG purposes

thanks for the input and we are treating as a single unit for cap gain purposes.  client does it as investment.

"client does it as investment"

That makes it sound like he does it more than a one time shot.  Sounds like it might have to go on a schedule C.