ばら撒いて means “to scatter” or “strew something widely,” often with the sense of spreading it around freely and dramatically. In the song, the singer says he will kick away the rainbow and scatter it across the sky, creating a fantastical image of turning the world into something dazzling for the person he loves.
The expression is memorable because ばら撒く is more vivid and energetic than the ordinary verb “to scatter,” and its ending -いて connects it smoothly to the next action in the lyrics.
The title 怪盗 (kaitō) means "phantom thief", the stylish gentleman burglar of Japanese manga and anime who leaves a calling card and vanishes over the rooftops. back number turn that character into a love song, and the setup is genuinely charming: "君の笑顔 盗む奴から 君を盗むのさ" (I'll steal you away from the people who steal your smile). He tells her to close her eyes and hold on to his arm, then promises to carry her over the night sky, leap across a city that glitters "宝石みたいな" (like jewels), ride the spring wind across the sea and kick rainbows apart to scatter them in the sky. It is a heist plan, and the loot is her.
Under all the fireworks, the line that matters most is a simple one: "君は今日も明日も君のままでいていいんだよ" (you can stay just as you are, today and tomorrow). When she tries to leave, he teases her with "ガラスの靴で 月にでも帰るの?" (are you going back to the moon in your glass slippers?), mixing Cinderella with Kaguya-hime, the Japanese folk-tale princess who returns to the moon. My favourite bit is the nerdy one: he says he would love to compare the version of himself who met her with the one who never did and write it up as a "論文" (academic paper), but the worth of "君の細胞全部" (every cell of you) could never fit on the page. It is over the top, and it knows it. For learners, notice how often 君 (kimi, "you") and 僕 (boku, a soft, casual "I" for men) appear: they set that warm, slightly boyish tone from the first line to the last "無い" (there's nothing [I can't do]).