POTENTIAL CONFLICTS; AMENDED CLRNCS AND RWY CHANGES PLAGUE A B757 CREW DURING THEIR KINSO 1 RNAV APCH INTO LAS; NV.

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WHILE BEING VECTORED FOR VISUAL APCH TO RWY 19L; WE ENCOUNTERED 2 TCASII RA'S WITHIN ABOUT 5 MINS OF EACH OTHER. THE FIRST WAS A RELATIVELY MINOR RA 'MONITOR VERT SPD' AS A BE1900 PASSED ABOUT 400 FT BELOW US. WE DID NOT SEE THE ACFT AND ATC SEEMED SLOW TO PROVIDE THE INITIAL VECTOR TO GET US AROUND THE TFC. THIS OCCURRED AT ABOUT 8000 FT MSL. WE WERE THEN CLRED TO 5100 FT AND VERY SHORTLY RECEIVED A 'CLB; CLB' RA. AT THE SAME TIME; ATC TOLD US TO TURN L AND CLB TO 5500 FT. THE TCASII VSI COMMANDED 2000 FPM CLB EVEN AS WE PASSED 5500 FT. I CONTINUED THE CLB TO 6000 FT AND RECEIVED THE 'CLR OF CONFLICT.' WE WERE NOW HIGH AND CLOSE TO THE ARPT AND CLRED FOR THE VISUAL TO RWY 19L. WE TOLD APCH THAT WE NEEDED TO WIDEN OUT TO DSND; BUT WERE RESTR DUE TO NELLIS AFB TFC. WE REQUESTED AND GOT S-TURNS; THEN TWR CHANGED RWY TO RWY 19R. THERE IS NO GS ON EITHER RWY 19L OR RWY 19R. THERE ARE VASI'S; BUT ARE ONLY GOOD CLOSE IN. IN ADDITION; APCH GAVE US A 'NONSTANDARD' CLRNC FOR THE KINSO ARR; 'FLY THE AIRSPDS AND AIRWAY; BUT DON'T DSND.' AND LATER; 'CLRED FOR THE KINSO ARR; BUT DON'T GO BELOW 8000 FT.' NOT THEIR BEST DAY.