Yes a Capital One 360 money market account is FDIC insured up to the same limits of a traditional checking or savings account.
You as a depositor into your Capital One 360 money market account is FDIC insured for an amount up to $250,000.00
If you have more than $250,000.00 in your Capital One 360 money market account then you're still FDIC insured but only up to the $250,000.00
So if something happens and you lose all your money then the FDIC will only give you back $250,000.00
If you're rich and have more than $250,000.00 it's best to have the extra money in more than one bank account to keep your money insured and protected in the event of a bank failure.