There is a difference of opinion concerning the reading of Waykhullu on Friday night after the 'Amidah. The most common custom for Ashkenazim, according to the Mishnah Berurah, is that it is preferable to read it with the congregation, because one requires a full congregation to give tesimony to Haqqadosh Barukh Hu. If it is not possible to say it with the whole congregation, it must, at least, be said with one other person.
He adds that there is an opinion that an individual may not say it on his own, and another opinion which says that he may, but does not need to stand. The Mishnah Berurah adds that it is preferable for an individual to say it but should not consider it to be testimony but simply reading verses from the Torah. The Hazon Ish is of the opinion that if one misses reciting it with the congregation one should not look to say it with someone else and that it is preferable in such a case to say it on one's own.
The custom for Sephardim is as mentioned in Ben Ish Hai. Hakham Yoseph Hayyim, 'a"h, states there, that after the 'Amidah of 'Arbith of Friday night, "Waykhullu" is said out loud while standing. Even one who prayed on his own is obligated to recite it because there is a deep Kabbalistic secret connected with saying it three times on Friday night. One who prays the 'Amidah BeYahid (not together with the congregation) must not say it less than three times either.
Sephardim who missed saying it with the congregation do not look for someone else to say it with, but say it on their own while standing.
(See Ben Ish Hai 2nd year, Parashath Wayera, Oth 9. Hazon Ish, O.H. 38:10. Mishna Brura, 268:19)
