Hello from JustAnswer.
In someone that acquires chlamydia from anal sex, it is possible for the germ to be transmitted to the genitalia, and then once affecting the genitalia, it can be transmitted by penile-vaginal sex. It is easier for a woman to transmit the germ from the anus to the vagina than for a man to transmit the germ from the anus to the penis, but it can be done.
In reality, though, this is generally not an issue, because whenever chlamydia is detected, the treatment for the germ will treat any chlamydia in any location in the body.
As for symptoms, many people that acquire chlamydia do not have symptoms, and this is true for an initial infection or if they get infected again. The risk is obviously related to the individual sexual history, but in certain populations, such as a young adult college student population, chlamydia can be found in up to 25% of people without symptoms. The absence of symptoms is not proof that someone is not infected with chlamydia, or indeed for any other STD.
If I can provide any additional information, please let me know.