No. You cannot catch chlamydia from a toilet seat or other surface.
There's no way to catch or pass on chlamydia from a toilet seat or other things such as as kissing and hugging, or from sharing baths, towels, swimming pools etc.
So there's no need to worry about getting or passing on chlamydia through a toilet seat or other surfaces.
The bacteria that causes chlamydia is usually spread through sex or contact with infected genital fluids (semen or vaginal fluid).
The most common ways that people get infected with chlamydia is through unprotected vaginal, anal or oral sex. sharing sex toys that are not washed or covered with a new condom each time they're used.
So if you know someone is infected with Chlamydia then you should use condoms and other protection when having sex.