My partner is on disability paid by blue cross. How do I report this?

If your partner paid the entire amount of the disability premium himself, then their disability benefits are tax-free. 

If your partner's employer paid all or part of the disability premium, then their disability benefits will be subject to income taxes. Your partner will get a T4A if this is the case.

He paid into the premiums for years through work and the entire money is coming from blue cross and they said no t4 would be coming.

So i don't claim his money from blue cross?

No, if the income is not taxable you don't need to claim it.