This is me, all over.
I can only reliably flirt when I don’t mean to, usually in talking to 60+ year old security guards in the library or chatty old men on public transit somewhere. That can be awkward, as I’m sure you can imagine.
On the other hand, my shyness can also be quite useful – I’ve perfected the “Help me! I’m shy and innocent and helpless” look, which gets me everything from directions and help with stuff I really should know how to do to forgiveness for faux pas like trying to enter the male security line at the airport in Jordan instead of sloughing off to the separate-but-equal ladies’ inspection area. It’s quite a useful little expression right there and I recommend you cultivate it.