The conditional mood (aurait) is only used in hypothetical situations (“Si j'avais su, je ne serais pas venu” = “If I had known, I would not have come”), or for a future tense with a past base (“Il a dit qu'il viendrait le lendemain” = “He said that he would come the next day”). It cannot be used in the sense of a habit like would can in English.
We just use the imparfait.
La rivière débordait parfois de son lit.
Some other notes on translation:
- Rivière is feminine, so la rivière.
- Inonder is transitive: you can say that a house is flooded (la maison est inondée), but to say that a river is flooding, you need to use another word, such as déborder (“de son lit” is more idiomatic but is optional).
Or we might use a different wording — still with the imparfait.
Il y avait parfois des crues.
If it's really important to put some emphasis on the habit, like “would sometimes flood” as opposed to just “sometimes flooded” in English, there are ways, for example:
Il arrivait parfois à la rivière de déborder.
But don't overuse this; most of the time, “would flood” and “flooded” are both best translated with a straight imparfait.