Maximum suction pressure is really only part of what is needed. The pump OEM should be able to provide information regarding the discharge pressure for the range of operating conditions as well as the seal chamber pressure. The seal chamber pressure depends upon the differential pressure across the pump as well as certain pump design factors.
You mentioned a flush fluid and a barrier fluid. It sounds to me as if the seal vendor has suggested using a fluid other than process to inject into the seal chamber as well as using a dual pressurized seal.
API Plan 32- Obviously the injected flush fluid must be compatible with the process, must not be injected at a rate that would dilute the process fluid, and be at a higher pressure than the seal chamber. This flush plan us often used when the process fluid has solids that would damage the seal faces, when the process fluid has poor lubricating properties/has a high vapor pressure, or when the process fluid is otherwise nasty- corrosive, toxic etc. Bradshsi makes a good point about the vapor pressure. Vaporizing fluid in a seal chamber is never good. The external flush fluid can help increase the seal chamber pressure as well as cool the seal reducing vaporization. A throat bushing in the seal chamber can be sized to help regulate flush fluid flow as well as seal chamber pressure. A box pressure of 25 psi above vapor pressure is a rule of thumb. Depending upon the process fluid and conditions it may not be enough.
API Plan 53 or 54- The pressure between the two mechanical seals must be higher than the seal chamber pressure, else process fluid will leak into the barrier fluid during operation of the pump. These flush plans rely upon some method of supplying a high pressure fluid between two mechanical seals in the pump. This flush plan is often used when the process fluid is nasty (as mentioned above, or is otherwise hazardous to personnel. Keeping the barrier fluid pressurized means that the process fluid cannot escape to the atmosphere. The 25 psi above seal chamber pressure is another rule of thumb with barrier fluid. 25 psi is usually a good enough margin to deal with changes in process conditions. This should also be reviewed- especially if you expect wild swings in process pressure. If so- discuss the use of an API Plan 53C flush plan with your seal vendor. A 53C uses a "piston pot" that references discharge pressure to automatically adjusts to changes. Or go for Plan 54- a lube oil skid used to support the seal.
Heat and pressure are always considerations with mechanical seals. Heat is usually dealt with by cooling the seal faces. In this case the Plan 32 injected flush fluid is usually chosen so that it is cooler than the process so it removes heat from the seal as it flows through the seal chamber. The barrier fluid (Plan 53 or 54) is chosen to be a good lubricator with good heat transfer properties. More often than not the barrier fluid flows through a circuit that includes a heat exchanger to remove heat generated by the seal faces. Pressure does distort seal faces, but there are ways to strengthen seal faces. Consult your vendor.