It is unclear and may depend on how you define chemical weapons.
Battle of Okinawa, 1945
The weapons used include
- chemical smoke mortar rounds
- white phosphorus grenades
An hour later another infantry assault was attempted, supported by 105-mm. artillery, light tank fire, antitank guns, heavy machine guns, 60-mm. and 81-mm. mortars, 4.2-inch chemical mortars, and bazookas; but the attack was again stopped by Japanese who hid underground during the heavy fire and then rushed back to their firing positions to meet the oncoming Americans.
From Okinawa: The Last Battle, Appleman, Burns, Gugeler and Stevens
It is unclear whether the chemical mortar rounds were designed merely to produce smoke to hide troop advances or were intended to harm enemy troops. From the text it seems they were probably intended to produce smoke through which US troops could move without being seen.
The 4.2-inch chemical smoke on the south side of Kakazu West was interspersed with high explosive artillery shells to keep the enemy pinned down. Under cover of the smoke the survivors of Company L pulled back off the hill to the gorge, carrying their wounded with them.
As well as flamethrowers and "chemical smoke", according to this account, the US army used phosphorus grenades
Colonel Maybury directed supporting fire in front of Company C, which quickly moved to the top without losing a man. It then proceeded leisurely and methodically to destroy the remaining Japanese with white phosphorus grenades and flame throwers. Only 20 of the 110 defenders escaped to the south.
It isn't 100% clear but this account can be interpreted as meaning that phosophorus grenades were used in an anti-personnel role.
The account doesn't identify the type of grenade, A more recent type is described as
The M15 White Phosphorous grenade is a bursting type grenade used for signaling, screening, and incendiary purposes.
The M34 chemical smoke grenade is the most versatile of all hand grenades. The grenade can be used for signaling, screening, or incendiary missions, or for producing casualties ... The filler has 15 ounces of white phosphorous.
Geneva Protocol, 1925
According to several sources 1, 2
The 1925 Geneva Protocol prohibits the use of chemical and biological weapons in war. The Protocol was drawn up and signed at a conference which was held in Geneva under the auspices of the League of Nations from 4 May to 17 June 1925, and it entered into force on 8 February 1928.
a sizeable fraction of its parties have reserved to themselves a right to retaliate in kind if chemical and/or biological weapons should ever be used against them by enemies or allies of enemies.
The protocol states
the use in war of asphyxiating, poisonous or other gases, and of all
analogous liquids, materials or devices, has been justly condemned by the
general opinion of the civilized world; and
this prohibition shall be universally accepted as a part of
International Law, binding alike the conscience and the practice of nations;
prohibition to the use of bacteriological methods of warfare and agree to be
bound as between themselves according to the terms of this declaration
According to ORGANISATION FOR THE PROHIBITION OF CHEMICAL WEAPONS
The general and traditional definition of a chemical weapon is a toxic chemical contained in a delivery system, such as a bomb or shell.
The Convention defines chemical weapons much more generally. The term chemical weapon is applied to any toxic chemical or its precursor that can cause death, injury, temporary incapacitation or sensory irritation through its chemical action. Munitions or other delivery devices designed to deliver chemical weapons, whether filled or unfilled, are also considered weapons themselves.
The toxic chemicals that have been used as chemical weapons, or have been developed for use as chemical weapons, can be categorised as choking, blister, blood, or nerve agents.
However this is a modern definition and the Convention referred to is a more recent one.
Chemical Weapons Convention 1992
Although produced 47 years after the date of the events in the question, this convention defines chemical weapons and so has some relevance.
White phosphorus does not appear in schedule one of CWC
1991 US View re phosphorus
A Declassified report mentions
POSSIBLE USE OF PHOSPHOROUS CHEMICAL WEAPONS BY IRAQ IN KURDISH AREAS ALONG THE IRAQI-TURKISH-IRANIAN
Some commentators have suggested that this phrase illustrates that WP is regarded as a chemical weapon by US intelligence.
According to the account given above, the US army did use flamethrowers, chemical smoke and white phosphorus grenades. These were probably not considered chemical weapons by the standards of the time. Nor by a strict interpretation of current conventions.
Speculation: A soldier defending his homeland against foreign invaders might take a different view if the invaders are using flamethrowers and white phosphorus grenades against him or her. Perhaps, literally in the fog of war, the unpleasant and potentially harmful smoke from white phosphorus grenades was described by Japanese soldiers as "poison gas".
(my emphasis throughout)