Firstly note Kelly isn't really considered a romance option and won't unlock the Paramour achievement and secondly, any gender can romance kelly XD
Chambers initially is quite formal with the commander, but eventually becomes more relaxed with the commander when he/she talks to her in a flirty manner. Continue to talk to her in a flirty manner, especially after each mission. She will then ask to feed your fish (I didn't have any fish from what I can remember but she still asked anyway.) Now, getting her to have dinner with you must have flirted with her and she must have asked to feed your fish. Once this has been achieved, the "Dinner" conversation will happen around recruiting Thane or completing his loyalty mission. Continue to flirt with her after completing recruiting/loyalty missions but, especially talk to her after recruiting Thane/completing his loyalty mission and you should eventually come to this conversation:
Kelly:- "I'm surprised by Thane's spiritual side etc. I don't know
whether to find him scary or sexy"
I then had the option to say either
"maybe both?" or "are you into aliens" I picked "maybe both?" (the
middle option, if picked dinner is not offered)
lot of women like bad boys"
Kelly:- "A lot of women like you?"
"thats not my thing"
Then asked if she wanted to have dinner with me
Kelly:- "goodness, i haven't stayed up that late since my college
days, i had a wonderful evening, thank you Shepard"
Now, if you manage to save her from the collector ship (i.e. only did one mission after your crew was captured (otherwise, I think you lose all crew) and removed her from the collector pod), she will invite you to your personal quarters via your personal messages and she puts on a sexy show for you! She will only dance for you if you have not FULLY romanced anyone else (i.e. sleep with them)