Can I apply for a US visa in Myanmar as an Indian citizen?

According to the US State Department:

You must schedule an appointment for your visa interview, generally, at the U.S. Embassy or Consulate in the country where you live. You may schedule your interview at any U.S. Embassy or Consulate, but be aware that it may be difficult to qualify for a visa outside of your place of permanent residence.

So the answer is yes, you may apply for a visa. However be aware that unless you are resident in Myanmar it could be difficult for the US consulate there to assess your personal situation and therefore a rejection becomes much more likely. I'd advise you to either become a local resident before applying or to apply when back in India.

I would add that applying for a visa here in Prague I wasn't even asked to prove I'm a local resident. My work contract and my bank statement was all they've needed, however this was at one of the least busy US consulates in the world and my passport is from a country that is a VWP candidate. Applying at the Yangon consulate as a non-resident with little local ties could be a dangerous proposition.

In addition the US Consulate in Myanmar states that:

All nonimmigrant visa applicants must show strong community, family, professional, and economic ties to Burma.

This shows that by default, they expect you to be a local.

P.S. There are situations where a particular US consulate routinely receives a lot of applications from neighboring countries because it's the closest consulate to where they live. In this case the consular employees would not be surprised to see documents from a third country and the above wouldn't apply.

You can apply for a visa in Burma, but at the visa interview, officers will want proof of ties to your country of residence, and if you don't live in Burma, you won't have Burmese documents proving ties.

US visa officers are mostly trained to deal with documents issued in the country where the embassy is located, so they may well not be familiar enough with Indian documents to be able to determine whether you have sufficient ties there and can safely be issued a visa.

So again, you can do it, but it's not recommended if you don't live in Burma.

I once asked the same question from an American consulate, and the answer I got was (paraphrasing):

You can apply anywhere, but applying in a different country than where you live may affect your chances of success. I am sorry, I am not allowed to tell you more.

@JonathanReez's answer basically says the same. I wrote this answer to point out something else:

When I was given this answer, I found it very frustrating because of a cultural disconnect between how paperwork is done in many European countries vs the US. I was used to relatively clear requirements: bring documents A, B, C and a notarized translation of D and you're good. (In practice: "You should've brought E too, in triplicate, and C doesn't have a stamp, so come back tomorrow".)

The American way of doing things is very different. There are not going to be very clear rules. You "just" need to convince the visa officer that you won't break the terms of the visa. There is no clear set of requirements to satisfy to guarantee success, and you can never be certain about how exactly they will make their decision. There is no rule such as "you can apply in country X if you present a residence permit for said country". Most of the responsibility stays with you, and if you are uncertain about how to fill out a form, or what documents to prepare, you won't get any help. Consulate workers are not allowed to give you information that would create the appearance that they are helping you succeed with your application.

You will simply need to make your own judgement about whether the visa officer will find your reason for applying in Myanmar acceptable.