First of all, despite my qualms, I'm more than happy to see a renewed strong showing for the Wild Cards book series. This new trilogy is just what I expect from competent genre fiction - page-turners with plenty of action. To an extent I can overlook characters of restricted depth.
Sadly for latecomers it looks like Inside Straight, the first of this new Wild Cards sequence, is already close to out of print.
That being said, I think you can pick up what's going on in Busted Flush without reading the previous book. The new-minted characters for this sequence are largely graduates of a superhero reality show, so basic character and relationship lines were drawn there and powers aren't necessarily re-explained in depth. Judging by the filling in for characters established in earlier Wild Card runs, some of which I only vaguely remember, there's enough information to work with.
There's a deliberate attempt to adult-orient the stories by putting the series at the front-line of contemporary global issues. In the first book the heroes who failed out of the reality show end up re-fighthing the gulf war. This volume revisits hurricane Katrina, the way the US treats "prisoners of war", and the situation in a non-specific Africa-zania.
There are, inevitably, tropes and cliches at work. In the tradition of none-more-literary sources than what I remember of X-Men comics, there's a wild card/mutant being held in a secret facility set up to hold people with powers and exploit them for military gain. The difference is that the power is driven by sexual activity. In fact, across the books there is more (fairly badly written) sex that you might expect from a superhero franchise, but that's a flaw that runs back through all the Wild Card series. Bolting on sex has been the basic knee-jerk method comics writers have used to slap a "look it's not for kids!" label on the content, so there is an hnourable tradition at work there. Keeping a little more up to date, there is a rash of lesbian characters, apparently now obligatory in prose genre fantasy. Gay men, however, are under-served.
The harshest criticism is for the pretty naked xenophobia on display. The series has ostensibly gone equual-opportunity globe-trotting but it's less-than-amazing that the darker characters are almost all non-American foreigners. English readers will almost certainly wince if not atively grind teeth because one of the characters who supports a major plot arc is notionally "British", as are his/her supporting characters. As written by an American the characterisation is a depressing litany of all the stock faults attached to the English - cold and unemotional, sexually ambivalent (it seems male homosexuality is still more a uncomfortable concept than its lipstick cousin), and cursed with bad teeth. There are gaping holes in understanding domestic English culture - such as what pubs are and when they open - and the attempts to write local dialogue falls under the inevitable curse of Van Dyke.
If you can forgive that and the sub-Buffy (or any current "teen" show written and performed by the proto- or actually middle aged) interpersonal relationships it's a reasobnably fast-paced, fun read.