All of this data is assuming you're using a full set of Savage Lynel Gear without any damage buffs on the items or through various equipment and such. Anyways...
Every time you get Flurry Rush, just switch to a spear. You attack nine times instead of four/five from the other weapons, which overall deals more damage. Every Flurry Rush in total will give you 270 dmg.
With headshots, things get a bit more interesting. After the initial headshot, run up to the Lynel and immediately use Stasis. This allows you to get two hits with two-handed weapons, four hits with swords and five hits with spears. Due to the average amount of damage a sword deals, it's your best option here. After the sword slashes, the stasis should run out. Mount the Lynel and switch to your strongest weapon (usually two-handed weapons), as all weapon types can attack five times here. When you're dismounting, if you're fast enough, switch to a spear. The second Link is thrown off, open the Paraglider and cancel it out with a bow before the paraglider actually comes out. The reason for this is because, as long as the Paraglider was registered (listen to the sounds), you can attack after shooting your arrows. Thus, you can get around three sets of arrows as headshots (shoot the back of Lynel's head) and then one last aerial hit with your spear.
Overall, the average damage you'll be doing with the mount strategy is 1,500. I don't know how much health Silver Lynels have, as I haven't fought any with the Champion's Tunic on yet, but I'm assuming that's pretty good.
In case things aren't exactly clear, I recorded a video with the strategy in action. It's not fully optimized, as it excludes the spear switches and triple arrows, but it gives a general idea of how it goes.