Both sentences make sense but have very slightly different meanings. “Aiming at” implies that buying the second house is a goal. “Seeking to” implies that he is currently looking for a second house. This difference mostly relies on the context of the conversation though and you could probably get away with either.

I agree with Brittany. I would add that where I grew up in the US, it is much more likely to hear "aiming to buy" than "aiming at buying" in this context.

An "aim" could be well in the future. I have an aim to buy a house before I die. I aim to buy a house someday, but now I like renting. I'm aiming to buy a house next year. (Suggests that I might already be seeking the house because it is relatively soon)

Thanks, Bob.

Is the second one