will an SSD work as well as an HDD like the Seagate SV35 for a surveillance system? >> yes
Is an SSD better to host and stream media like FLAC and videos than an HDD? >> no, you won't see the video playback any faster...just better seek time, but ssd is not cost wise since it cost way more expensive than mechanical harddrive
Will it prevent my home network from lagging due to HDD boot up? >> if you mean will you have faster boot time, then yes, ssd will speed up your boot time
An SSD will last longer physically, just by right of it not having any moving parts. They do wear out through use, but modern SSD's will last long past the point of their obsolescence so thats not a concern.
If you want to record surveillance footage, a HDD is a much better option. For instance a 3TB drive can be had for ~$150, while to get that much capacity with SSD's (you would need multiple unless you use PCI storage devices) would be more like $1500. Also there would be little benefit to to using an SSD anyway, the extra speed wouldn't help in this usage.