Is there any kind of legal action I can pursue for being forced to work with a stomach flu?

No, there is almost certainly no legal action. The law does not require employers to provide employees with paid sick days, or even to allow them  unpaid time off for illness or medical treatment. (Unless, that is, the condition is sufficiently serious, which a stomach flu would very rarely, if ever, be, that the employee can and does take leave under the Family and Medical Leave Act--which also requires that both the employer and employee qualify under the act; you can find the criteria for FMLA leave at the U.S. Department of Labor Website.)

Apart from situatations invoking FMLA leave or its state-law equivalent, however, an employer does not have to let an employee take time off from work for illness, and could terminate an employee for missing work due to sickness. This may well be unfair, but it is the law.

If you did have sick days, however, you should have been allowed to use them, so long as you followed any company policy (e.g. call-in policy) in regards to them; sick days which you earn are part of your compensation, and a refusal to allow you to use them effectively means you are not being paid everything due you. Unfortunately, even if this were the case, it is highly unlikely that you could claim or sue for enough to make a lawsuit worthwhile--for example, if deprived of the use of one sick day, in theory, your recovery might be one day of wages.