Is it possible for Inosuke to become a Hashira with his beast breathing?

Yes. He have the strength and skill for it

Beast Breathing is a quite unique Breathing. Mostly due to Inosuke being the only know human that can force his organs and muscles to work the way the Breathing requires AND have the senses for it

In terms of power, Inosuke is more than stronge enough to be a Hashira

According to Douma, Kanao is at very least relative to Shinobu (probably higher considering her performance against UM2 and she could survive a bit against Muzan)

Meanwhile, Inosuke is able to do the same or even better than her against Douma. Aswell being able to do some damage to Muzan

The simple fact he could stand his ground against Douma already give him the level of non-Marked Hashiras

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Therefore, yes.

Despite having a self-thought Breathing, Inosuke is powerful enough to be a Hashira (an actually good one). If the demons didn’t dissapeared after Muzan’s defeat, then he would be one of the best options available

Have a great day!