Make discreet eye contact with her on a regular basis.
The best and most subtle way of flirting with that special girl at work is to indicate your interest by looking at her. This does not mean you need to burn holes through her with your eyes. Instead, find a way of catching her eye as you pass her desk, giving her a soft, discreet smile before you release eye contact.
Offer her a compliment on her attire or her perfume.
If you find yourself in a meeting with her, sit near her and tell her that you really like the shirt she is wearing or the color of her shoes. These are subtle ways of expressing your admiration and flirtation. If you want to be a bit more daring, tell her you really like her perfume. Ask her what kind it is and tell her that you would like to buy some for your girlfriend.
Recommend a book or film that has suggestive overtones.
In conversation with her, drop a subtle suggestion that she see a particular film that you think she would like. For instance, you might recommend "The English Patient," a very romantic and sensual film that would be perceived as suggestive and flirtatious to her.
Buy her a coffee and bring it back to her after lunch sometime.
A woman loves the attention you show her, especially when she has not asked you specifically for it. So, sometime when you go out to lunch, take the liberty of bringing her back a frappucino or latte from the coffee shop. This is thoughtful and flirtatious at the same time.
Send her a flirtatious email.
As long as you are discreet and non-threatening in your approach, you can send her a nice morning email on Friday, for example, wishing her a lovely TGIF and an enchanting weekend. Avoid asking her plans or inviting her to make some with you. The mere thoughtfulness and suggestiveness of the email will allure her.