The Vikings while being loosely based on history isn't historically accurate, and in some instances characters seen in the show lived over a 100 years apart in real life.

The Ecbert seen in Vikings is probably based on King Egbert of Wessex who ruled from 802-839. Wessex was one of the seven anglo-saxon kingdoms that existed in Britain. The Kingdom of Wessex could be described as the predecessor of the Kingdom of England.

The vast majority of our information about the Kingdom of Wessex comes from the Anglo-Saxon chronicle, an original version of the chronicle no longer exists, however various copies of it exist which give broadly similar, but slightly different information. Despite this we can say that hereditary succession most definitely took place before Egbert.

Cynric, the second king of Wessex, is described as either being the son or the grandson of Cerdic the first king.

Cynegils was either the son or nephew of his predecessor Ceowulf.

Cyneglis had a son, Cenwalh who also became king of Wessex. However between the death of Cenwalh in 672, and Egbert dying in 839 no kings of Wessex were succeeded directly by their sons.

However other Anglo-Saxon kingdoms did have sons succeed their fathers, for example in 779 in East Anglia, Aethelberht II succeeded his father Aetherlred I.

I would also like to mention that although it was unusual for a son to inherit, for a member of the family to inherit would be the norm. A majority of the Kings of Wessex, and Kent (where Egbert was from) were succeeded by a relative, just not their son.

This was because during this period in England the system of primogeniture (where the eldest son would inherit) was not yet established. While the system of succession changed from place to place and time to time, and the succession of most kings are not described in detail in any primary sources. Typically a king would have succeeded his predecessor by winning an election by the nobles. Therefore instead of a young son inheriting a brother would be more likely to inherit, therefore power would remain within the same family.

It should also be mentioned that, due to the divine right of Kings not being a concept that was widely popular at the time, and also due to the small size of the countries. It was possible for a new family to overthrow the old ruling family, and this happened far more often than it did during the medieval era, although a relative of the old king inheriting was still far more likely.

The main thing Egbert did differently from his predecessors was to live for a long time, dying at the age of 68. Meaning his son would have been old enough to succeed, in addition to this Egbert also made it very clear in his will that he wanted to be succeeded by his son. Also before his death he bribed the bishop of Winchester and the Archbishop of Canterbury to support his son's claim to the throne.

Sources:

The Anglo-Saxon chronicle by An Unknown Scribe in Wessex in the 9th century

Anglo Saxon England by Sir Frank Stenton

The Earliest English Kings by D.P. Kirby