No, you are trading "firm capital" and as a member of the firm, your individual trades are not subject to the wash sale rule. You receive a K-1 statement from the firm which shows your P&L, of which a copy is sent to the IRS. The wash sale rule applies to retail traders who trade as a business and have not made the "mark to market" election with the IRS for the specific account they are trading. Having a 56 license does not make you exempt from the wash sale rule on your OWN retail account, you still have to file the necessary paperwork. For more information on the wash sale rule and making the "mark to market" election, see link below, and obviously ask professional advice from an accountant, preferably one that prepares taxes for traders: http://www.irs.gov/taxtopics/tc429.html
Only a 475 election or some other mark-to-market regime (1092, 1256) eliminates the hassle of wash sales. If you are a class b member of the firm you generally will receive a schedule k-1 for your share of the firm's taxable income or loss. Absent some mark-to-market regime, the firm may still be subject to wash sale limitations on equity and equity option positions which impacts your share of taxable income or loss but you will not necessarily see the impact by simply looking at the k-1. Wash sales from your personal accounts are still an issue even if the firm makes a 475 election as the two are considered separate trades or businesses.
Prop trading firms who skip the Section 475 MTM election have tax problems potentially causing inequities for their LLC member traders over wash sale rules. Here's an example. Trader 5 takes a loss and Trader 6 buys back the position within 30 days triggering a wash sale loss adjustment. Trader 5's loss should be added to Trader 6's cost basis. I guess the firms don't do that and they keep the sub accounts separate based on economics only. (Otherwise Trader 6 would be charged with Trader 5's loss.) But that would not be in compliance with IRS rules. The prop trading firm should calculate wash sales across all it's sub trader accounts based on substantially-identical positions. It's a much better idea for prop trading firms to elect section 475 MTM - and I believe most have - to avoid this tax mess. Remember independent contractor prop traders get a 1099-Misc and that's a fee not a share of trading gain or loss.