The only problem with "Daisy Chaining" refers to two or more power strips plugged into each other. People tend to overload them, forgetting they have 16 pieces of equipment plugged into one circuit.
Otherwise it's OK.
A typical surge-suppressor is comprised of a metal oxide varistor.(MOV) High voltage surges are clamped by the varistor to safer lower voltage levels. If you daisy chain your power strip surge protector, by plugging it into your suppressor receptacle, it's OK, you are just adding another MOV or two of protection.
Hopefully your receptacle surge device gives off an audible alarm upon failure. Some have a pilot light only, the problem with those is, they are usually hidden behind your equipment rack.
He is a little info on transients.
Most surges occur when devices with motors - hair dryers, refrigerators, water pumps - shut off. Suddenly the energy these devices were consuming is diverted elsewhere in the form of excess voltage. Surges also happen when the electric company switches power from one geographic area of the grid to another, as supply and demand in the region changes. Thunderstorms and lightening are the most dramatic and destructive causes of power line problems.
Only 40% of surge problems are generated outside the home or office by events such as lightening, utility grid switching, line slapping, etc. 60% of all electrical surges or transient voltage is generated within the home or office. Surges are caused by elevators, air conditioners, vending machines, copiers, large computers, even lights turning on and off will cause rushes of power and transient voltages back up the line.
Computerized appliances and electronics can be damaged or destroyed by over-voltage surges or spikes. This includes computer equipment and peripherals; electronic equipment such as stereos, TVs and VCRs; household appliances including washers, dryers, refrigerators, dishwashers, microwave ovens, food processors, blenders;(you get the idea)
and other electronic devices such as fax machines, telephones, and answering machines. Any electronic device that contains a microprocessor is susceptible to damage from transient voltages.