'Lawforce' is Mr Universe's slang for "Alliance Law Enforcement". These are federal police (who can arrest you anywhere), as opposed to local police or private security.
After all, that was what the Alliance did, wasn’t it? It controlled. It ran every aspect of life in the civilized parts of the ’verse, from what you ate to what you bought, from the level of society in which you moved to the rules that governed your daily routine. The Alliance, with its troops and its law-enforcement operatives and its tame corporations and its bought-and-paid-for politicians, held everything tight in its tentacles. Even out on the Rim you couldn’t escape it.
Firefly: The Magnificent Nine
A 'flag' would be a bulletin notification on the Cortex about wanted fugitives and/or their ship.
“Well, seems you got no choice but to keep my goods in your hold and
get the ruddy ’ell out of here.” He tapped the tablet with his finger.
“This is a bulletin, just got sent out all across the Cortex. Feds are
hot on your tail. Seems you people have something they want. What is
that, I wonder? What you got on board they’re so flaming interested
in?”
Firefly: Big Damn Hero