A NEAR COLLISION OCCURS BTWN 2 VFR ACFT 8 MI S OF WST; RI.

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WE WERE DEPARTING RWY 25 FROM WST; RI. WE TRIED TO GET A CLRNC ON THE GND; BUT COULD NOT REACH PVD APCH. SINCE IT WAS SEVERE CLR; WE DECIDED TO TAKE OFF VFR AND PICK UP THE IFR ASAP IN THE AIR. AS SOON AS WE DEPARTED RWY 25; K WE CALLED APCH AND GOT A SQUAWK (XPONDER) CODE. HE THEN TOLD US THAT WE HAD TFC AT THE R SIDE 'ALT UNKNOWN.' APCH TOLD US TO TURN TO HDG OF 180 DEGS. WE DID NOT SEE THE OTHER ACFT YET. ATC TOLD US TO TURN FURTHER L TO 150 DEGS. AT THIS TIME WE SPOTTED THE TFC AND SAW THAT WE WERE PASSING HIS ALT AND THAT THERE WAS NO CONFLICT. APPARENTLY; THE ACFT (A BARON) WAS VFR AND WAS NOT TALKING TO ANYONE. THERE WAS NO CONFLICT OR PROB. THE BARON CALLED OUR ACFT AND WAS CONCERNED ABOUT THIS. I DO NOT KNOW ANY SOLUTION OTHER THAN TO USE 'SEE AND AVOID CONCEPT' AND TO BE VERY VIGILANT IN PROX OF UNCTLED ARPTS. SAFETY IS ALWAYS FIRST IN EVERYTHING; ESPECIALLY AVIATION. I LEARNED THAT ALWAYS BE VERY ALERT IN ANY AIRSPACE -- ESPECIALLY UNCTLED. SUPPLEMENTAL INFO FROM ACN 548393: I WAS FLYING IN LEVEL CRUISE FLT WATCHING FOR TFC AND MONITORING PVD APCH CTL. MY ACFT IS EQUIPPED WITH A SKY WATCH TFC ALERT SYS (SIMILAR TO TCASI WITH NO CONFLICT RESOLUTION). I HEARD ACFT X ON THE FREQ ADVISING PVD APCH THEY HAD DEPARTED VFR OFF WST AND REQUESTED THEIR IFR CLRNC. THEY ALSO ADVISED THEY WERE CLBING TO 4500 FT TOWARD HTO. I THEN NOTICED MY SKY WATCH DISPLAY TFC AT 8 O'CLOCK POS LOW AND CLBING. I HEARD PVD ADVISE THE CREW OF THE JET TFC 1 O'CLOCK POS AND 1 MI AT 5500 FT (ME). A PLT RESPONDED 'LOOKING' OR SIMILAR. I DIPPED MY WINDS TO ALLOW THE JET TO SEE ME. HE ANNOUNCED THAT HE SAW THE TFC. I RETURNED TO LEVEL FLT AND WATCHED THE JET CLOSING RAPIDLY. IT WAS APPARENT TO ME THE JET WAS NOT GOING TO DEVIATE. I MADE A HARD TURN SOUTHWARD AND THEN HEARD A PLT OF THE JET ANNOUNCE TO PVD APCH THAT THEY WERE TURNING TO AVOID THE TFC (ME). AS THEY DID SO; THEY CLBED THROUGH MY ALT. I CALLED THEIR OPS. I FOUND OUT THEY SHOULD HAVE DEPARTED VFR; AND THEIR ACFT IS NOT EQUIPPED WITH TCAS. THE PERSON I SPOKE WITH SAID THE INCIDENT WOULD BE REVIEWED. THE JET CREW SHOULD HAVE SIMPLY LEVELED OFF UPON NOTIFICATION OF NEARBY TFC UNTIL EITHER HAVING VISUAL CONTACT OR BEING ADVISED BY APCH CTL THAT TFC WAS NO LONGER A FACTOR. WITHOUT SKY WATCH AND LISTENING UP; THERE COULD HAVE BEEN A CLOSER NEAR MISS OR A COLLISION.