Generally not - Arrivals access is not a oneworld privelege.
Assume you may by flying Bangkok Airways domestically (most likely to USM Koh Samui?) If so, from memory the domestic are of BKK airport is separate so I dont believe you could access the oneworld lounges even if you were able to gain access.
Bangkok Airways has its own lounge at BKK (accessible to all pax I believe) but dont think it has showers.
When I went through a few years ago there was also a Domestic Transfer path that was separate to the main immigration path.