Many years ago I ran the 59 mile wilderness trip from Pandale to the Hwy 90 bridge with my son and three other friends. Here are a few things that you MUST be aware of on that river.
1. Do not try to run it with less than 100 cfs of water flow. To do so is to invite misery. Same goes with the season. June through September would be brutally hot.
2. Flash floods are extremely dangerous in this stretch of river. ALWAYS camp way up on the river bank.
3. The Pecos has an interesting feature in that the water is very alkaline and "slime" doesn't grow on them like in most rivers. This makes them VERY abrasive. When I went, the word was do not make this trip in a cheap plastic boat. There are instances where canoeists tried to make the run in those old Coleman canoes and were stranded deep in the canyons because huge holes were rubbed into the boat. I can't help you on what types of KAYAKs would withstand the abuse.
4. Back when I made the trip, there were only two springs along the way where you could replenish water supplies. The alkaline water is unpalatable and boiling it doesn't change that.
Once you launch at Pandale, you're committed. Without a satellite phone, you are not going to call for help and there are VERY FEW places you can get out anyway as you are in canyons most of the way with no road access.
The book entitled "The Lower Pecos River" mentioned in the post above is available on Amazon. Highly recommended. Now, bear in mind that I made the trip many years ago in my younger days. Many things could be different now, but I doubt the basic info above is outdated.
I consider this trip a highlight of my outdoor life. The scenery is breathtaking. The fishing is unbelievable (side note, we only kept the fish you see in the picture for eating one night on the trip). The Indian cave paintings are among the best preserved in the country. It is guaranteed if you do it at the right time with good water flow and weather and plan your trip well, you will never forget the experience! Good luck.