I just got my Petroleum Club card
My company supply engineering and specialist products to primarily the Oil Industry so it seems your connection can be quite loose. I spoke with my boss and it took a while to get the company registered on the AF/KLM list but after that it seems you just have to apply.
Just wanted to add that on the P-club section of the KLM website (which is very limited) it is very clear that the benefits are only for the card holder. I'm going to test this at AMS later this month when I fly with my partner to Stavanger - and attempt to blag lounge access for us both.
Current offers for P-club at the moment are:
upto 50% off Le Meridian hotel rates
upto 25% off Accor hotel rates
(both of which have been unavailable when i looked

)