Can I resume a romance with Kelly Chambers?

Yes, it's possible to have a romance with her, and she's one of the hardest characters to romance. The Wiki has the complete info:

Shepard re-encounters Kelly on the Citadel...
...her death fate can be avoided if upon reuniting with Kelly, Shepard persuades her to "change her identity".
She will disappear for a few missions. She will eventually reappear donning a new look and ask you how she looks.
After the Cerberus raid on the Citadel, she can be found again in the Dock area of the Citadel...
If Shepard didn't have dinner with Kelly during the events surrounding the Collectors, Kelly will be absent even if she survived those events.
If Kelly was taking care of Shepard's fish during the Collector Attacks, she manages to take them when she left, and will return them to Shepard after the Commander runs across her on the Citadel.
If Shepard is not involved in a romantic relationship with any other character, it is possible to pursue Kelly after she changes her identity and the Citadel is raided by Cerberus.

So if you satisfy those half dozen-ifs, half of them based on the last game, yes, you can romance Kelly. It sounds like you're most of the way there, though.

Note that unlike Mass Effect 2, romancing Kelly gets you the Paramour achievement this time.

She is available, and I have done it. Not only do you end up sleeping with Kelly in her container unit, but she expresses how happy she will be when she is together with Shepard after "this is all over". If you go back after that she gives you more dialogue, such as remembering how she danced for Shepard and too bad she doesn't have that outfit anymore. So evidently the save game remembered that, and it is a prereq for romance this time around.