I am traveling to Yerevan-Armenia from London with my daughter with a Refugee Travel Document issued by the UK. We have a few hours stay in Boryspil airport in Kyiv.
Do we need an airport transit visa?
Kyiv Boryspil airport has an international transfer area, so there's no need to go through passport and customs control between your flights. See "International to International Connections" on airport website
Persons who have a Refugee Travel Document (Convention of July 28 1951) often (but not always) require a visa based on their nationality stated in the document. Some countrys require some form of endorsement in the document that the person may return to the issuing country.
2021-06-15: Entry regime to Ukraine for foreign citizens | Ministry of Foreign Affairs of Ukraine
If you are the holder of a refugee document (according to the Geneva Convention) or a stateless person, you always need a visa to enter
The linked 'visa to enter' page implies that a visa requirement is also needed for a transit visa, but since the OP has not stated their nationality/citizenship this cannot be checked with the visa checker that is offered on that page.
Stateless persons have a Certificate of identity (alien's passport): 1954 Convention Relating to the Status of Stateless Persons. Some countrys require some form of endorsement in the document that the person may return to the issuing country.
The 1954 Convention was adopted to cover those stateless persons who are not refugees and who are not, therefore, covered by the 1951 Refugee Convention.