Tiber Septim was Dovahkiin, right? He had dragon blood flowing through his veins, and it was he who formed the Empire and such.

With the Dragonborn also being Dovahkiin, he also has dragon blood flowing through his veins. Are the two related? If so, does that make Dragonborn a potential candidate for the Imperial Throne?

There is no indication that the Dovahkhiin is a Septim, and you don't need to be related to a Dragonborn to be a Dragonborn. (and the septim emperors aren't descended from old Tiber anyway)

I'm thinking Dovakiin might be more in line for high-king.

The Dragonborn is well positioned to become the next emperor.

This because the empire is very fragmented right now, and there is no one individual compelling enough to make the remaining nations rally.

Only a Dovakhiin has the inborn power and evidence of divine blessing to make all the warring factions put aside their differences and focus on the Thalmor

Right now the Thalmor are waiting to deliver their final blow

Sorry, its a new line of emperors. Either he/she would need to muscle out the next heir or take White-Gold amidst a bunch of infighting.