The communist insurgency in Burma actually predates the establishment of the military dictatorship. There were also in fact two communist insurgencies. Also, the ideology of the military dictatorship was not exactly "communist", if by communist you mean marxist-leninist like many communist regimes of the time were. The situation was, as is always the case with Burma, pretty complicated. In this reply I will try to explain the origins of the different communist movements and their differences.

Under British colonialism, disgruntled Burmese intellectuals frequently met and discussed political issues. Their group was called the Dobama Asiayone, and its members were the Thakins, or masters, as they wanted to become the masters of their own country. They brought together traditionalist Buddhist nationalist elements and fresh political ideals, among which was Marxism.

Massive strikes against the British took place in 1938, which would lead a year later to the creation of the Communist Party of Burma (CPB). Among its leaders were members of the Dobama Asiayone Aung San, Thakin Soe and Thakin Than Tun. In its early years The CPB remained largely underground and launched attacked against the British until 1941, when the Japanese empire invaded Burma.

In 1940, Aung San left Burma to attend the conference of Indian National Congress, but when he tried to come back to Burma, he was forced to exile by the British for inciting revolt. He went to China and tried to gain the support of the Chinese Communist Party, but was captured by the Japanese.

With Japanese support, Aung San formed the unit of the Thirty Comrades, the predecessor of the Burmese Independence Army (BIA) created in December 1941 in Thailand. Among the 30 comrades was Ne Win, future leader of the military dictatorship of Burma. The BIA helped the Japanese during their invasion of Burma and fought alongside them. Meanwhile, Thakin Soe and the other members of the CPB, led a resistance movement against the Japanese.

Aung San became more and more disillusioned with the Japanese and realised that supporting them would not win Burma’s independence. In early 1945, as the tides of the war were turning against Japan, Aung San and his comrades joined the allies, and formed an organization called the Anti-Fascist Organisation (AFO). This group was comprised of the CPB, the BIA, and the socialists of the People’s Revolutionary Party, led by U Nu, who would also become an important figure of independent Burma. The AFO was later renamed the Anti-Fascist People’s Freedom League (AFPFL).

After the defeat of Japan and the end of the war came the question of independence, as Burma was still considered a British colony. Aung San favored negotiating with the British and travelled to the UK to meet Clement Attlee and discuss the terms of independence. Meanwhile, in the BCP, there were ideological dissensions, as Thakin Soe thought that only revolutionary struggle could liberate the country, while others such as Thakin Than Tun kept cooperating with the AFPFL.

In 1946, Thakin Soe decided to go underground and to lead an armed struggle against the government of Aung San, and his movement was rapidly declared illegal. His faction was called the Red Flag Communist Party (RFCP), as opposed to the White Flag Communist Party (though they never gave themselves that name) of Thakin Than Tun. Allegedly, the RFCP was inspired by Trotskyism.

Aung San was assassinated in 1947, and after Burma became independent in 1948, the civilian government was dominated by the AFPFL, led by U Nu. Just two months after independence, due to ideological disputes it was Thakin Than Tun’s turn to rebel against the government and start a guerilla with the White Flag Communist Party. Its political line was Stalinist, though there later was a split among the party between revisionists and Maoists during the Sino-Soviet Split.

The civilian government stayed in power for about 14 years, until was overthrown in 1962 in a military coup by Ne Win, the former comrade of Aung San in the Burmese Independence Army. If you are interested in learning about the reasons behind the coup, I have written another reply about it : https://old.reddit.com/r/AskHistorians/comments/l9zgcu/myanmar_has_become_the_central_focus_on_many_news/glls4u6/ .

The ideology of the military junta led by Ne Win was called the “Burmese Way to Socialism”, it combined some socialist principles as well as Burmese nationalism and Buddhism. The communist rebels, who continued their armed struggle against the central government, were considered by Ne Win as “vulgar materialists”.

I hope the answer was not too long. There were a lot of different actors and political movements during this era, and as we saw pretty much all political parties and movements in Burma considered themselves either socialist or communist, but many conflicts arose, due to ideological disagreements or power struggles. This is without even mentioning the ethnic conflicts, which add yet another layer of complexity to the political history of Burma.

My main sources for this comment are :

The State in Burma, Robert H. Taylor

The River of Lost Footsteps: A Personal History of Burma by Thant Myint-U