What's the meaning of "No law less than ourselves owning" in this Whitman's poem?

Solution 1:

Own is being used in the archaic sense here, see:

Own

archaic with object Acknowledge paternity, authorship, or possession of. ‘he has published little, trivial things which he will not own’ - OLD.

The fact that they will not own any law other than themselves means that they will submit to no law less than themselves.

Taking your original phrase:

No law less than ourselves owning

You could rephrase less poetically to mean:

Answering to no one else but ourselves.

Solution 2:

The poem uses complement fronting. What this means is that the complements of the verbs, which would normally appear after them, have been moved to a preverbal position. (The last line reverts to a normal phrase order to bring the poem to a close.)

So, instead of clinging together or never leaving the other or alarming misers, menials, priests we see:

  • together clinging
  • the other never leaving
  • misers, menials, priests alarming.

The Original Poster's example, No law less than ourselves owning, if rendered with a normal phrase order, would read:

Owning no law less than ourselves, ...

There is an archaic use of own, as mentioned by @Gary meaning to recognise. Here are some examples:

  • to own your mistakes
  • The Scottish lords were not to serve beyond the sea against their will, and were pardoned for their recent violence, in return owning allegiance to Edward.
  • ... when each chief was a monarch owning no law but his own will, no master but the King of Heaven.
  • a man who reproaches himself for lack of gall, and pours out the most biting irony upon an egotistical court-circle seeking only its own advantage, and owning no law but external decorum

The word less is sometimes used with a meaning similar to other, especially if there is some kind of negation involved. Here's a definition from Dictionary.com

  1. in any way different; other:

He is nothing less than a thief.

Consider:

  • It was none less than Bob himself.
  • It was none other than Bob himself.

The Original Poster's example can therefore be understood as meaning:

Recognising no other law than ourselves.

Here, of course, law refers not to a single rule, but to a ruling authority.