I have no physical need of a chair
Not sure if she needs the word "physical" but it is there to contrast with the mental need she describes later in the poem. Why does she not need a chair? Because
I can double my body anywhere
Yes, witty follow-up. The body can find rest in itself, by acting upon itself, "doubling" as it were. Self-reliant, it can rest on a "stone" or the "ground," no chair necessary. But what the speaker needs is to "feed my wit/ With beauty and complexity." The emphasis here is on the feeding, and not the having. For if she thinks she already possesses "philosophy," then she were "high man without complexity." "Man" here means primarily humans, but I think by using "man" she also takes a dig against male complacency at having the answers to life. The complacent man, the "high" man, would fling himself on "any natural sod/ To scan the zenith and remember God." In other words, the "high" man would rest on his possession of wisdom. When he scans the zenith, he does not discover anything new, but merely remembers the old idea of God.
This reading about human complacency is confirmed by the next lines:
But it is needful man shall strive
With tortured matter, so to keep alive.
Life, for Wickham, resides in striving with tortured matter, and not with resting on any natural sod. It is a dynamic philosophy of will, not a static wisdom of possession. After this statement of its point--its need--the poem goes on to elaborate in six uninspired lines:
Idle man would never live to age:
He would run mad and die in rage.
When fat accumulations cloy,
War brings her sword to ravage and destroy,
That through the smoke of the consuming real
Man sees a clearer and more sure ideal.
The boldness here lies in the thought of war as a necessary destructive force to wake man to his ideal life of constant strife, but the expression of the thought is mundane and clumsy. The rhymes cripple the poetry.
Returning to the beginning of the poem, I now find it rather misleading. The central contrast in the poem is between those who rest in complacency and those who ever strive. The opening lines, however, posits a contrast between resting in a chair, and resting without a chair. I think this misdirection is caused by the common problem of discovering an arresting start for a poem, and then wandering away from it in the subsequent argument. One is naturally reluctant to delete the wonderful opening that gives rise to the poem, even if it does not lead logically into it. Wickham's editor comments that she seldom revised her poems. Her poems show the freshness of spontaneity, as well as its flaws.