At many brokers you can buy immediately with the proceeds of a sale. However, both the sale and purchase would not settle for 3 business days, so you could not turn around and sell again until the previous sale/purchase settles, unless you already had enough cash or margin for the 1st purchase after the sale. Otherwise if you made a profit doing that (selling, buying, selling) before the first sale settled without cash or margin to cover the buying, you would get a warning or worse for what I think is called a "Free Ride" (since you had no money in the 2nd stock when you sold it).

To day trade at all, you need settled cash or margin, and in the U.S. to day trade more than 3 times within 5 business days you need a margin account containing at least $25,000 in assets.

It takes typically 3 days to settle the cash from a sale, so you would not be allowed to make multiple purchases with the same 10K

If there is let's say $10,000 of initial cash deposited into a Brokerage account and a stock is bought then sold so now there is $10,100 total then the $10k is used the same day to buy stock then sold again the same day, is this allowed or only one buy/sell can take place that day with the same $10k?? (Essentially flipping stocks multiple times a day).

Thanks.