タイムフライヤー is a creative Japanese-English compound meaning “one who flies through time.” It is an especially memorable phrase because it is not a standard everyday expression.
In the song, the singers call themselves “time flyers” as they race through time together, giving the phrase a dreamy, cinematic feeling that fits the story of Your Name.
The song opens by begging for time. "もう少しだけでいい" (just a little more is enough) comes back again and again, and then turns into "もう少しだけ くっついていようか" (shall we stay close together a little longer?). It is a simple request, repeated until it sounds almost stubborn, and I love that it never gets fancier than that.
Then the singer gets playful with borrowed English: "僕らタイムフライヤー" (we are time flyers) and "時を駆け上がるクライマー" (climbers racing up through time). He calls time a game of hide and seek, says he is done with getting lost, and promises "やっとこの手が 君に追いついたんだよ" (at last this hand has caught up with you). The best moment is about her tears. He wants to stop them, she refuses, and he realises crying when happy and laughing when sad means "君の心が 君を追い越したんだよ" (your heart has overtaken you). That last line is a lovely way to say feelings move faster than the person holding them.