Can you be paid a flat rate per day and have it be paid out on your check as a ‘commission’?

It is legal to pay you  a flat rate regardless of hoursworked so long as:
1) You are paid at least minimum wage--divide the hours worked by the pay received to see if this is the case; if it's not, they'd have to pay you more to bring you up to minimum wage, and you could contact the state department of labor to file a complaint if they don't.
2) If you more more than 40 hours in a workweek, or 8 hours in a day (in your state; most states don't have this), you are paid at a higher rate for the additional hours. Granted, in a situation like this, it can be difficult to determine if that is the case, but if you regularly work more than 8 hours in a day or 40 hours in a week, there is a good chance they are violating the overtime rules and you should be paid more--you may again wish to speak to the department of labor if your regularly work that much. (If you much more often than not worked 8 or less hours per day, or 40 hours or less per week, as a practical matter, it would likely not be worth filing a complaint.)
Much depends on the flat rate you are paid. Minimum wage in your state is $10/hour. If you were paid $80 or $100 per day, there's a good chance that they be violating the minimum wage or overtime rules when you work more than 8 hours/day or 40 hours/week. On the other hand, if you are paid $200 per day, you've basically being paid for 20 straight time hours or 8 straightime and 6 overtime hours--there's a good chance that unless you were working truly excessive hours that they would be in compliance with minimum wage or overtime rules. Therefore, you need to alos make a judgment call about whether you are being paid well enough to cover their legal obligations (and to make complaining about the pay counterproductive) or not.
Finally, it doesn't matter what they call the pay--it can be called wages, or commission, or bonus, etc.--so long as they in practice honor their legal obligations.