I think we're missing the point here, which is that philandering and flirting are different things.
Philandering means actually having sex with a succession of people other than your partner.
Flirting is just friendly conversation motivated by attraction.
So it depends on the meaning you want to convey.
However, we wouldn't say philandering with X, because philandering is a general activity, rather than a description of your actions with one person. And it is a little old-fashioned, so there might be better words in this situation anyway.
Hello, Hyperion. Namlan's example - Mary is philandering with Peter - is unusual. When people use the word, they are usually talking about some male subject. I think the noun "philanderer" is more common than the verb "philander": George was a philanderer. Jack was caught philandering once again.