Do I need to report FMLA -short term disability insurance payments?

Yes. The payments should be included in the W-2 you received from the employer and is taxed just the same as regular wages.   

Family and Medical Leave (FMLA)

I got 8 weeks of paid STD for when I was on maternity leave. Is that already included on my W2 from my employer or will I receive another W2 for it? I'm trying to do my taxes online and it didn't ask me for my FMLA or STD/LTD payments or anything like that. I'm just curious if it's already calculated in or would it not be since the insurance company paid me and not my employer. 

It depends on whether you paid for the short term disability (STD) or whether your employer paid the premiums as a benefit to you.

1. If you paid the premiums for this STD then it will not be taxable and you can file your return with your W-2 from your employer; OR
2. If you did not pay for this insurance, then it could be included in your W-2, or if paid by a third party insurer, you could receive a second W-2. Check with your payroll department to be sure.

You can read more details at this link: Are Short Term Disability Payments Considered Earnings?