Essentially, it can't be 'proved'. The usual argument wheeled out to demonstrate the 'falling domino' principle is the near-simultaneous rise of communism in Vietnam, Laos and Cambodia in the 1970s. But trying to conceptualise that as a domino effect is pretty facile.

The big problem, as I see it, is that trying to argue that it was the rise of the Vietnamese communists that triggered similar movements in Cambodia and Laos elides the true historical context: that all three countries had been part of French Indochina, and that their civil wars/communist insurgencies were more directly part of the decolonisation process and the postcolonial struggle, rather than being some kind of ideological chain reaction. Those movements worked together, sure, and they all stemmed from the Indochinese communist movement, but they had distinct characters and motivations — and their relationships weren't always cordial.

The domino theory relies pretty heavily on a monolithic understanding of communism that's as bizarre as it is pervasive. How do you reconcile that with the Sino-Soviet split, or the ideological gulf between Maoism and Ho Chi Minh Thought? How do you connect those eastern communist ideologies with Castroism? Yes, all roads ultimately lead back to Marxism-Leninism, but communism is a broad church whose factions seldom co-exist happily.

Ultimately, it's a piece of political theory based on flawed observations and teleological assumptions. China and Russia became communist states, then so did Korea. So the Korean War is stage 1 in the advance of communism in the east. Suddenly Vietnam is in flames and the red flags are flying, and Cambodia and Laos look to be heading that way too — stage 2. Where next? Indonesia? Thailand? Malaya? And what about Africa? Meanwhile, Castro has taken power in Cuba and suddenly South America is in play.

Lots of this postwar Red Scare-type panic about the 'rise of communism' (and modern neocon thinking, which owes a lot to it) fails to acknowledge that the primary reason there were insurgent communist movements in so many countries during the 1950s-1970s is that you've got dozens of new countries being created for the first time as part of a global decolonisation process. In each of those political and social vacuums, you've got political movements emerging all vying to shape this new state in their image. It's just easier to draw a big scary red line around the globe because the rhetoric of these national communist movements have common intellectual roots (up to a point) and are using similar buzzwords.

Edit: fixing mangled final sentence.

/u/k1990 is absolutely correct, it cannot be proved. However, from the mid-1950s to mid-1960s there were many arguments that can be, and were used to, justify the fear of communism spreading from Vietnam to Thailand to Malaysia to Indonesia, etc.

Malaysia at the time was fighting the Malayan Emergency, a communist insurrection supported (although not overtly) by both the USSR and the PRC. However, most of the guerillas and their supporters were ethnic Chinese. The Indonesian commmunist party supported the insurrection and so did then-President Sukarno.

Speaking of the Indonesian communist party, at that time it claimed to be the third largest in membership, behind only that of the USSR and the PRC. Its leaders called for arming the populace to support the confrontation against Malaysia. While Sukarno didn't publicly support this, it created significant worry among the anti-communists.

So even if the pieces may not fall in sequence like in a domino, there was real concern about the spread and rise of communism in southeast asia.