Q: Is it possible to have "Red Man Syndrome" (RMS) with oral Vancomycin? 

Answer: Unlikely but yes

"Red man syndrome" (RMS),  occurs mostly with parenteral administration of vancomycin. Oral administration of vancomycin  does not usually result in systemic absorption. However, for some patients, especially those with impaired renal function, oral administration may lead to detectable serum levels and RMS.

References: 

1. Rao S, Kupfer Y, Pagala M, Chapnick E, Tessler S - Systemic absorption of oral vancomycin in patients with Clostridium difficile infection.- Scand J Infect Dis. 2011;43(5):386

2. ergeron L, Boucher FD, Possible red-man syndrome associated with systemic absorption of oral vancomycin in a child with normal renal function. - Ann Pharmacother. 1994;28(5):581.