bk19702 is correct. An API Plan 14 is likely what you want.
However, I am making some assumptions in this conclusion. First, because you are using a single seal, I assume your process fluid is not hazardous. Second, because you do not mention cooling, I assume the process fluid is not at an elevated temperature (>60 C/150 F)
If API682 does not recommend Plan 11 for vertical in-line pumps (as opposed to vertical pumps in general), they are almost certainly referring to single-stage pumps. Aside from some extremely rare 2-stage specialty in-line designs; the phrase "vertical in-line pump" generally means a single-stage pump.
The pressure in the seal chamber is going to depend on the type of impeller. Because you are referring to API 682 standard, I assume you have an API pump with a closed impeller (with wear rings). In the vast majority of cases, a closed impeller will have balance holes from the suction side to the back side. These holes even out the pressure on both sides of the impeller and reduce the thrust load on the bearings. Therefore, the seal chamber will normally operate near suction pressure.
The key thing with a vertical pump flush plan, as flexibox points out, is that you need to vent the air out of the seal chamber. The seal faces are at the top of a closed cavity and you need to get rid of the entrained air so the faces do not run dry.
This is the problem with an API Plan 11 in any vertical pump. There is no venting of vapor from the seal faces. Even if you include a provision to manually vent your seal chamber before start-up you will be depending that a) the operators do it correctly every time, and b) that no additional vapors will enter the seal chamber during operation.
Once the venting is addressed, the seal flush plan for a vertical pump is the same as any other pump. You need to provide adequate flow to dissipate the heat generated by the seal, and if you are pumping a fluid that is subject to flashing (light hydrocarbons) you may need to increase the pressure in the seal chamber to prevent vaporization of the process fluid.
API Plan 14 can do all of these things. As bk19702 points out, the plan is self-venting. Then, for the flow rate and pressure, you just need to adjust the orifice sizing in the piping from the seal chamber back to suction and perhaps adjust the throat bushing clearance.