HPV or the Human Papilloma Virus infection is the cause of viral warts. There are over a hundred different strains of HPV. Different strains of HPV tend to favour different sites e.g. the strains of HPV that cause genital warts are often different from the strains that cause finger warts or feet warts. So the risk of spreads from of warts from the finger to the genitals is very small. If your flat or plane warts are on the face or limbs for example, the risk of getting genital warts will be very low.
Genital warts are predominantly spread by sexual contact. Avoiding high risk sexual contact is the best way to prevent genital warts infection. There are HPV vaccines available that significantly reduce the risk of genital HPV and cervical cancer. They are recommended for teens and young adults and even some adults. You can speak to your doctor more about HPV vaccination.