im a student at mingo job corp a goverment program and was wondering if they can legaly force us to take a flu shot?

This is a legal action.  Most employment relationships are what is known as "at will". This means that basically the employer can hire or fire someone for any reason or no reason whatsoever, as well has increase/decrease salary/hours, promote/demote, and generally impose requirements as they see fit. In turn, you can work for an employer, or not, your choice. The exceptions to the this would be if there is a stated company policy covering this, or there is a union/employment agreement that governs, or this situation has arisen due to some type of discrimination.