MIL-PRF-5606J, What does "J" means? Does it equal to MIL-PRF-5606?
I don't know this specification, but the letter at the end indicates the revision number of the document. J would be the 10th revision/ 11th edition. 
Note that there are often also intermediate publications with minor improvements called 'Amendments' 

Version J was published in March 2018. 
The version before, H, was published in June 2003 with Amendments in 2003, 2005 and 2006, and an additional notice in 2011. 
(source)

Referring to MIL-PRF-5606 can thus mean the first edition of the specification, or it can be a generic reference where the edition is omitted.

It depends on the context, but since the original publication must have been ages ago, my bet is on it being a generic reference.