How can I get to Kathmandu from Myanmar using land transport?
Yes, such a trip is doable, via India.
Reasoning the route
As I wrote in this post, it is currently impossible to reach Nepal via land from China, leaving only border crossings with India in question.
The route from Tibet into Nepal is open again, meaning that you could in theory also consider routes via China. However the option via India still seems a lot more straightforward to me.
You do not specify your nationality nor preferred means of land-travel, so I will assume that visa are no problem and any means of transport besides flying are fine.
From Myanmar it is possible to get to India (more below). There are also border crossings with Thailand (open), Laos and China, but that would include huge detours. In fact since India does not have a border crossing with China that is open to non-locals or non-pilgrims, any itinerary not directly through India would include a detour through all of China via the Karakorum highway into Pakistan and then India.
So Myanmar - India - Nepal it is.
Getting from Yangon to the border
Citing from Wikivoyage again:
A land border crossing exists between India and Myanmar at Moreh/Tamu. There have been confirmed reports of travellers crossing into Myanmar from India (and vice-versa), with their own transport as well as with permits arranged in advance. It is no longer required to have a permit to visit the Indian state of Manipur, but an MTT permit is required to enter or leave Myanmar at Tamu. This permit is readily available from MTT in Yangon (who will require you to book a tour guide) or a number of other agencies (who will not) for USD 80-100 per person. Most agencies require 20 working days to arrange the permit (but in some cases can do it faster), and can have it delivered to the border so that you do not need to return to Yangon to collect it.
("MTT" stands for "Myanmar Travel & Tours")
This is confirmed by e.g. plenty of posts in the Lonely Planet Forum, e.g. post 414 reports from experience and recommends another travel agency as of 2016, this blog reports similar from 2015 and this one of 2016 reports a hassle or two but made it as well. So I do not see any problems to this part of the journey judging from recent reports.
Traveling within India (and to Kathmandu)
Now I'm no expert on India but Rome2Rio tells me that Manipur to Kathmandu can be driven. I also see train connections all over the place in India and then you could cross into Nepal by bus or renting a car with driver.
The only thing left open would be permits for North-Eastern India. Wikivoyage has to say:
Note that entry into the states of Sikkim, Arunachal Pradesh, Nagaland, Manipur and Mizoram requires a Protected Area Permit (PAP) for non-Indians and an Inner Line Permit (ILP) for Indian citizens. Permits are issued by the Ministry of Home Affairs, but the easiest approach is to get your Indian visa with a special endorsement allowing travel in the state you wish to visit. Individual travelers are generally granted 15 days (extendable once), but are allowed access only into major towns and sights; travels off the beaten track generally require a registered tour group of four or more people.
As of 1 Jan 2011, the Government of India has decided to exclude the states of Manipur, Mizoram and Nagaland from the Protected Area regime notified under the Foreigners (Protected Areas) Order 1958. This programme is being trialled for one year. However, it is advised that travellers still print out the relevant news articles from local news sources such as the Nagaland Post and Morung Express to show to border officials.
Another post in the Lonely Planet forum claimed that said program has been extended to December 2017, so you should have no issues passing through, but might be better to check on this one again before you depart.