The Thai government is set to open two temporary refugee camps in Ranong and Chumpon. These are two cities on the southern end of the Myanmar-Thai border. According to Thai news outlet the Thaiger:
Refugee camps will be set up in Ranong and Chumphon which border Myanmar’s southern-most region. Most of the violence has been around 1,300 kilometres north in Yangon where the military regime recently imposed martial law in 2 townships.
The shelters will be temporary, commander of the Thep Satri Task Force Santi Sakuntak told the Bangkok Post. He says the migrants will be sent back to Myanmar once the situation eases.
The Thai-Myanmar land border stretches 2,400 kilometres. It’s unclear why just 2 camps are being set up in the south rather than at major border towns like Tak’s Mae Sot district.
As for other border crossings and illegal crossings, the Thai approach has been to send them back. Again from the Thaiger:
Last week, the Human Rights Watch called on Thai authorities to stop expelling asylum seekers at the Myanmar border, citing a recent incident where Thai officers caught 8 Burmese people who were crossing the Ruak River from the border town Tachileik and sent them back to their home country.
Thailand’s officers have been cracking down on migrants long before the military coup in Myanmar due to concerns about the potential spread of Covid-19. Patrol along the Myanmar border tightened back in December after hundreds of Burmese migrants at a fishing hub in Samut Sakhon tested positive for the virus, sending Thailand into a wave of infections.
I got 14 days visa free to travel Thailand.
I don't think this applies during the Covid-19 pandemic. This visa free arrangement applies to arriving by air, not by land, according to thaiembassy.com (note: this describes the situation before the pandemic):
Citizens of Myanmar are now allowed visa-free visits to Thailand for up to 14 days if arriving by way of air travel into the country. The recent reciprocal agreement has been implemented last August 11, 2015 which also gives visa waiver privilege to Thai nationals who wish to travel to Myanmar for a maximum duration of 14 days.
At the moment, there are 23 airports across the Kingdom of Thailand where travelers may arrive via a commercial aircraft. The regulation, however, in all the land borders or immigration checkpoints remains the same as Burmese citizens are still required to obtain proper visas if entering Thailand by means of land travel from a neighboring country.
Travelling by air, however, is severely restricted. Furthermore, the visa exemption is restricted for Myanmar nationals, according to the IATA Travel Center (click on Thailand):
- Suspension of visa exemption for nationals of Cambodia and Myanmar with a normal passport.
Even if you were to get a Thai visa, you would be required to quarantine upon your arrival in Thailand. As a foreign national, you would have to pay for that yourself with additional constraints such as having a negative PCR test for Covid-19 before your flight, a health declaration from a physician and an insurance policy that covers at least $100,000. See for example this page of the Thai embassy in the Hague.
So your best option is probably to aim for the temporary refugee camps named at the start of my answer. How that works in practice probably isn't clear yet, the news article was published less than a day ago.