I am not a tax professional. All I know is from personal experience in doing my own taxes as someone who is self-employed. So please do your own research, speak to a CPA if you're not sure about something, and take this with a grain of salt.
First off: You have to pay taxes on all self-employment income. Even if a company doesn't report the income, it's still your legal responsibility to report it.
In my experience, working just as a self-employed contractor (so NOT an s-corp, or LLC, or anything like that), you will pay taxes on all gross (pre-tax) income. So the money you get from Niteflirt, most likely, will not have taxes taken out of it because they state on their website, "Flirts are not employees of NiteFlirt."
Even if you make $20,000 and they send you a 1099-K, if the boxes on the form for state tax and federal are empty, they didn't pay any. And even if Niteflirt did withhold some taxes, you can't assume this was the right amount of tax for Niteflirt to withhold, so when you file your taxes you would be calculating that on your return yourself (or with a CPA).
If you have paid taxes before (even just regular, not self-employed taxes), you will need to be making quarterly payments on your self-employment income. How? Either get with a CPA, or look up the IRS.gov 1040-ES form (estimated self employment income), go through the worksheet, follow their online steps to pay the estimated amounts. There are deadlines for those, so you'll want to set reminders (next one is sometime in September, if I remember correctly). Otherwise there can be penalties (not huge but definitely inconvenient).
If you want to be absolutely certain, talk to a CPA now to get your quarterly payments setup. When it comes time to actually file your taxes make sure you bring your copy of the 1099-K, income documentation (checks, invoices, whatever to keep track of what you made), and your estimated payments (which your CPA should have on file you did it with them). Your CPA should go through an individual tax return (like, a 1040, probably), and probably a Schedule SE, and probably a Schedule C, which are all used to calculate self-employment tax. If your quarterlies were estimated appropriately you might get a return, or at the very least, not have to pay more in taxes in a huge chunk at the end of the year.
This is super glossed over because I don't want to say too much and offer bad information but I had a bad experience going into tax season blind (hadn't ever filed before), and my tax person entirely skipped my Schedule SE, and Schedule C, and I wound up having to go through the process of redoing all the forms, filing by myself, and finding out I had over $600 in self-employment tax that I owed. I really don't want anyone to have to deal with that.
So just really make sure that either A. You really, really, are thorough when you do your taxes, and figure out what you need to fill out to do them yourself. Or, B. Get a CPA and make doubly sure they understand how self-employment tax works. Any CPA who tries to tell you that you either don't need to make quarterly payments, or don't owe any self-employment tax is probably doing something wrong, so get a second opinion.
EDIT: Also, the amount you should be putting back is hard to say. A safe bet is usually 25% of your gross income.