Since you are asking about withholding, I assume that you are a W-2 employee, not an independent contractor.
How you will be taxed depends on why you are working remotely (telecommuting). New York has a "convenience of the employer" rule. If you are working in Kansas because the employer wants to have an employee or representative in Kansas for business reasons, then you are working remotely for the employer's convenience. In that case, your income from the job is Kansas income, not New York income. You will pay only Kansas tax.
But if you are working remotely because you prefer to live in Kansas instead of New York, then you are working remotely for your own convenience, not the employer's convenience. In that case, New York treats you the same as if you actually worked in the New York office. The income is considered New York income and you would pay New York tax on it. Since you are a Kansas resident, all your income is subject to Kansas tax, no matter where the income is from. So you would also have to report the income on your Kansas tax return. But you should get a credit on your Kansas tax return for part of the tax that you pay to New York, to eliminate the double taxation. (I'm not familiar with Kansas taxes, but I assume the credit would be equal to the amount of the Kansas tax on your New York income, so you would still be paying the full New York tax, since the New York tax rate is higher.)
As far as withholding is concerned, if you are going to be paying Kansas tax, you want to have Kansas tax withheld from your pay, and the income should be reported as Kansas income on your W-2. If you are going to be paying New York tax, you want to have New York tax withheld from your pay, and the income should be reported as New York income on your W-2. If the employer has a Payroll department that is separate from HR, I strongly recommend that you discuss the withholding with Payroll, not HR. You are more likely to get accurate answers about withholding from Payroll.
Please note that New York income tax is not a flat rate. It has graduated rates in brackets, like the federal income tax. The rates range from 4% to 10.9%.
You should not have to pay New York City tax, and should not have any New York City tax withheld. Your W-2 should not show any New York City income. New York City income tax applies only to residents of New York City. Nonresidents of the city do not pay New York City income tax, even if they physically work in New York City.
