There were four main ways that I identified that revolutionary armies in South America got their weapons and military supplies. I’ll primarily focus on San Martín, but I will also mention Bolívar when relevant.

The first way was by using the arms troops and officers already had or were able to purchase, steal, and pick up along the way. For most of the Bourbon period, the basic colonial defense strategy was based on colonial militias rather than regulars. The general goal was to maintain a modest defense of strategic points at the lowest possible cost, and peninsulares and creoles often provided much of the money for weapons, supplies, and uniforms. In Buenos Aires, this fell to the primarily creole merchant class who deeply resented the steep demands that military service put upon their estates. Following the British invasion of the Río de la Plata in 1806 and 1807, there was a general militarization of rioplatense society, which shifted the balance of power away from the traditional colonial elite. Therefore, much of the Río de la Plata was already militarized in 1810 with weapons and munitions imported from Spain or smuggled in. Following the outbreak of the civil wars, Chilean soldiers fleeing the fall of the first independent government in Chile brought their weapons with them to Mendoza where they rendezvoused with San Martín’s troops. Furthermore, many plebeian and African soldiers did not use firearms at all, instead fighting in irregular lancer units; this was especially common among Bolívar’s famous llaneros. Sometimes, armies even used indigenous weapons. For instance, indigenous units helped turn back an army sent by Buenos Aires to take Upper Peru at the outbreak of the war. As the wars dragged on, the armies scavenged for weapons and ammunition whenever they moved into new areas.

Secondly, San Martín’s troops were able to produce some weapons themselves. As San Martín assembled the Army of the Andes, he enlisted the help of the whole province of Cuyo. Women helped produce uniforms. Local caudillos and gauchos donated horses, mules, and cattle. Mines turned over raw materials needed to make weapons and gunpowder. And famously, Father Luis Beltrán, who had significant knowledge of chemistry and manufacturing, constructed a basic munitions factory that employed 500 or more workers. Under his direction, the factory created or repaired dozens of artillery pieces, hundreds of rifles, swords, bayonets, munitions, and gunpowder. Fortunately for San Martín, he also crossed the Andes and continued producing weapons in Chile for the assault on Peru.

Commonly, the armies captured weapons from strongholds or those left behind by retreating forces. For example, the new Chilean navy under the command of Lord Cochrane captured the Spanish town of Valdivia along with "50 tons of gunpowder, 10,000 cannon shot, 170,000 musket balls, huge quantities of small arms, 128 pieces of artillery and a prize ship, the Dolores" according to the book Cochrane in the Pacific: Fortune and Freedom in Spanish America (pg. 73). Major victories often included seizures of weapons caches.

Finally, the armies received weapons from foreigners. This was less important in southern South America than it was in the Caribbean, which was closer to British and American bases. Many of the creole elites had connections to British intellectuals and merchants who were sympathetic to their causes. Their contacts raised money and supplies for the revolutionaries. As Karen Racine writes in her article “‘This England and This Now’: British Cultural and Intellectual Influence in the Spanish American Independence Era”, Britain “adhered to an official policy of neutrality. In practice, however, Spanish American agents in London openly recruited military personnel for their armed forces. Between 1817 and 1819, London newspapers were filled with advertisements for buttons, muskets, tailors’ services, leather goods, and everything a young man would need to outfit himself. Bell’s Weekly Messenger spoke of the “South American mania” that gripped London streets” (pg. 434). Additionally, various mercenaries in the Americas were able to receive arms shipments or even reinforcements from home. For example, the famous British Legion joined Bolívar’s army after the Napoleonic Wars, bringing weapons and materiel with them. Like the British government, the United States, though supportive of revolutions in the Americas, remained neutral because it was unclear if the revolutions were actually going to succeed. Overall, though there is documented support and examples of weapons trafficking, the weapons and supplies shipped from Britain and the United States were not as significant as one might think. As Chasteen and Halperín-Donghi explain in The Contemporary History of Latin America, “although the volume of clandestine purchases of weaponry from Great Britain and the United States never amounted to much, its importance to the Spanish American insurgencies shows how limited their resources always were” (pg. 59).

And that is really why you don’t hear much about arms or trafficking in the books on the revolutions: the armies did not receive overwhelming foreign support and were exceedingly impoverished and poorly equipped. Soldiers’ weapons wore out, broke, or became unusable and were never replaced. Officers complained that their troops did not have weapons or their weapons were in a total state of disrepair. Men went into battle without weapons and picked them from among fallen comrades. They quickly wore through their shoes and uniforms, which were never replaced because generals lacked money for supplies. One foreign soldier in Bolívar’s army described the rest of the force as “young negroes and mulattoes, most of them mere boys, seemingly not more than thirteen or fourteen years of age, tottering under the weight of their muskets and wearing nothing more than a piece of linen around the loins. Some might wear old military jackets but would be without pantaloons. Some would be bareheaded, while others might wear straw hats or hairy caps…” (Quoted from Blanchard’s Under the Flags of Freedom: Slave Soldiers and the Wars of Independence in Spanish South America, pg. 128). Troops often lived under near starving conditions. The armies were always short on money. Bolívar’s troops for instance only received 25% of the wages they were owed during the entire Peru campaign, and very few of the common enlisted men ever received the wages they were promised. But conditions for Spanish royalist forces were comparable. They too remained reliant on the local opportunities and foreign connections for financial and materiel support. Although we tend to denigrate "great man history", in my view, the most impressive of the liberators’ feats was holding their armies together despite such adversity.

edit: typos