It's a good bet that Box will have boatable flows from late March thru May.
Flow information from Box Canyon Dam can now be obtained from the Siskiyou County General Services webpage. See this Box Canyon Discharge Flow Rate to download a pdf graph of readings for one month. If the webpage is down you can try calling 530-842-8250 during regular business hours and ask for flow information. Everyone has been nice and helpful in obtaining the information.
The Sacramento @ Delta gauge displayed below is 40 miles downstream from the put-in. Because of myriad tributaries, this gauge will read much higher than actual flows in Box canyon. However, as the season progresses, the flow in box canyon will be an ever increasing percentage of the total flow at the gauge.
Paddlers will sometimes post the height of the Cantara Gauge on Dreamflows.com (The Cantara guage is the stick gauge at the end of Box Canyon on river left). Boatable levels are from about 4.5' to over 6'. Difficulty is class 3 at the lowest levels and steadily increases through class 4 at 5' to class 4+ at the higher levels..
Reports give the public a chance to report on river conditions throughout the country as well as log the history of a river.