(The king of Israel) may take wives and pilagshim from the entire territory of Eretz Yisrael. The term 'wives' implies women who were married with a ketubah and kiddushin; pilagshim, women who were not given a ketubah and kiddushin. With the act of yichud alone, the king acquires her and relations with her are permitted him.
What is the legal source (Talmudic or otherwise) used by Rambam to claim that the king of Israel can acquire a pilegesh with yichud alone?
The Rambam understanding comes from the gemara in sanhedrin 21 that a pilegesh is without kedushin and nisuin, so then how would he aquire her,yichud which is the derech of acquiring without the special din of kedushin and nisun. See the Rambam in the beginning of hilchkos Ishus.
Rav Chaim Kanievsky in his Kiryas Melech page 246 writes the source for taking anyone is from a Tosefta in Sanhedrin 4:2.