Please do NOT flush it down the toilet! Yeesh! It can clog the toilet and is terrible for the environment. If you are worried she is going to use your DNA maybe you need to rethink who you are visiting with... I always remove the condom, wrap it in tissue, and throw it in the garbage dumpster. If you are really that concerned then bring your own box of condoms with spermicide lubricant, the spermicide will kill the sperm. But I did some looking around after reading the OPs post and it looks like sperm does not last long at all outside of the body so unless she used it immediately it wouldn't work.
For their own protection from potential pregnancy & child support payments, it is suggested that guys take cum filled condoms with them, or otherwise safely dispose of the sperm, after sex with a SP.
Regarding spermicides:
"Spermicides cause irritation and according to the CDC, studies have shown that spermicides increase the risk of HIV. Contraceptive Technology states that spermicides have a failure rate of 18% per year when used correctly and consistently, and 29% under typical use.[2]"
"...condoms that are spermicidally lubricated by the manufacturer have a shorter shelf life [18] and may cause urinary-tract infections in women.[19] The World Health Organization says that spermicidally lubricated condoms should no longer be promoted.
"...Nonoxynol-9 has a number of possible side effects. These include irritation, itching, or the sensation of burning of the sex organs (either partner), and in women, urinary tract infections, yeast infection, and bacterial vaginosis.[21] These side effects are uncommon; one study found that only 3-5% of women who try spermicides discontinue use due to side effects.[22]"
http://en.wikipedia.org/wiki/Spermicide
At one time N9 was thought effective vs HIV since it killed HIV in the lab, but:
"From 1996 to 2000, a UN-sponsored study conducted in several locations in Africa followed nearly 1,000 sex workers who used nonoxynol-9 gels or a placebo. The HIV infection rate among those using nonoxynol-9 was about 50% higher than those who used the placebo; those using nonoxynol-9 also had a higher incidence of vaginal lesions, which may have contributed to this increased risk. Whereas these results may not be directly applicable to lower-frequency use, these findings combined with lack of any demonstrated HIV-prevention benefit from nonoxynol-9 use have led most major health agencies to recommend that it no longer be used by women at high risk of HIV infection. The WHO further notes that "Nonoxynol-9 offers no protection against sexually transmitted infections such as gonorrhoea, chlamydia."[2]
"Regular use of nonoxynol-9 appears also to increase the risk of infection with sexually transmitted human papillomaviruses (HPVs) that can cause cervical cancer.[3][4] In one of the studies, researchers at the National Cancer Institute also reported that the increased likelihood of HPV infection caused by N-9 was mitigated through the use of carrageenan-based lubricants mixed 1:1 with N-9. Two consumer products containing carrageenan, Divine 9 and BIOglide, prevented detectable HPV infection in the study."
http://en.wikipedia.org/wiki/Nonoxynol-9
