The current constitution is the 2008 Constitution of the Republic of the Union of Myanmar. The three post-colonial Constitutions - 1947, 1974 and 2008 - are available online in English on the Myanmar Law Library website (open access)
The Comparative Constitutions Project (open access) has a terrific tool for comparing the three versions of the Constitution Article by Article.
The Constitutional Tribunal of the Union of Myanmar was established in 2011 by the Constitutional Tribunal of the Union Law (Law No 21/2010). It is housed in the same building as the Supreme Court. Its role is to adjudicate constitutional issues and disputes, review the constitutionality of legislation and executive action, and it acts as the final authority on matters of constitutional interpretation (s 12 of Law No 21/2010). Neither individuals not civil society organisations can bring cases to the Tribunal; it is confined to hearing matters brought by the Government (the President or Chief Minister), Legislature (the Speaker of either House) and the Chief Justice of the Supreme Court (ss 13-17 of Law No 21/2010). The Supreme Court retains jurisdiction to hear constitutional rights-based claims by individuals, but may not interpret the Constitution.
The Submissions and Decisions database on the website of the Tribunal contains an incomplete set of the decisions of the Tribunal. To date it has heard very few cases. Some decisions are in English only, others in Burmese only.
For an excellent explanation and critique of the Tribunal, see Melissa Crouch, 'Dictators, Democrats, and Constitutional Dialogue: Myanmar's Constitutional Tribunal' (2018) 16(2) International Journal of Constitutional Law (2018). Available on open access on SSRN. In this article, the author reflects on the implications of the role of the Tribunal as a forum for constitutional dialogue between and among military dictators and democratically elected representatives.