The stock A/C system in these trucks does NOT take well to R134a...especially the systems in the 'Burbs and even more especially with front and rear air. I've got a 1990 GMC 'Burban with front and rear air that I tried to convert to R134a a few years ago. It was a stupid waste of time and money. The thing wouldn't cool below 60 degrees at the vents. I wound up buying some R12 off eBay. System runs great with the R12.
If you are intent on converting you will need more than what the crappy universal kits have. You need good, heavy duty replacement fittings, new accumulator, new TXV for the rear unit, new orifice tube and a replacement condensor that is efficient with R134a. You'll need to flush the old mineral oil out of every line with solvent and use a compatible R134a oil. New o-rings will need to be installed as well that are compatible with the new refrigerant and oil. I believe your year 'Burban came with the A6 compressor which is a good unit. If the system is not compromised, you can probably flush the mineral oil out of it and reuse it. If your compressor is the A4, then it may need to be replaced...it's not a great compressor to begin with.
Anyhoo, as you can see, it's not that easy or cheap to convert. I'm not telling you this to scare you or anything, but I have seen people use enough of these universal conversion kits with very poor results (sometimes disastrous) and had to fix them that they are ahead to either keep on with R12 or do the conversion right the first time. If your system is clean and not damaged, you may be ahead to find some R12 and have it charged. However, the dual system does take upwards of 70 ounces of refrigerant...not inexpensive.
Kevin