Can I watch a siyum on skype or listen to it over the phone in order to eat fleishig during the nine days?
Hearing a siyum or watching it online is not going to permit eating meat during the nine days. The reason why one may at meat when at a siyum, is not because he heard the siyum, but because he is partaking in the seudas mitzvah. However if he isn’t partaking in the seudas mitzvah, he is not permitted to eat meat.
May we all merit seeing the rebuilding of the Bais Hamikdash in the near future
Maharam Brisk 1-133, Teshuvos V’hanhagos 1-300, Mekadesh Yisroel 256, Yabia Omer 4 O:CH 42. (See Rivivos Efrayim 1- 296, and Bais Avi 1-16, who say regarding a siyum on erev Pesach, that since the day of a siyum is like Yom Tov therefore even if the bechor was not there for the meal he may still eat. Most poskim however disagree with this. Aside from this, it would seems that this idea cannot be applied to the nine days, as everyone would agree that a person that did partake in a seudas bris or siyum, that he cannot eat meat the whole day, but only at the actual siyum or bris. Therefore someone who isn’t present for the seuda may not eat meat. See Kovetz Halachos chap.9 ftnt 36, that also says this idea.)