I would recommend that you read the Flashpoint book if you want all of the details.
From what I got in the book, it's been 3 weeks (including the time they pass in warp space).
Mengsk arrive at Char and tells Valerian to surrender Kerrigan. Valerian says no, so Mengsk and his half of the fleet fires of Valerian's half of the fleet (what is left of it).
After that, they run to Deadman's Port to find shelter and make repairs on the Bucephalus and the Hyperion. Some of Mira's men, with the help of the Bartender, reveal their location to Mengsk, so they have to run.
Valerian suggest that they go to Doctor Narud's secret lab, so they can do some tests on Kerrigan and figure out if she is 100% human or if she has a chance of reverting back. Narud betrays Valerian and releases Hybrids to stop Raynor, Valerian, and Kerrigan. Kerrigan goes berserk when Narud almost runs away with the Xel'Naga artifact, kills one hybrid, a hundred Marines, and Anabelle (the engineer from the Hyperion).
Then Valerian suggests that they go to the Umojan Protectorate to study Kerrigan in one of his labs that no one knows about yet.