Although you will get some of the seals in the skill up party as they drop randomly and it is a good idea if you want some, that doesn't necessarily mean they will let you take them. All it takes is a couple of people saying no, like a tank or refresher and you are out of a party.
And to the OP again, I am wondering as to, why do you want to farm KS? Getting KS is a slow process even for a party. I get about 2 KS every time I join an EXP party, skill up party, farm or kill EP mobs. I get about 2 every 2 hours approximately at the rate mobs are killed. Given you need 30 seals to do a KS30 run and if you are looking to make money from it, say do Desert Storm with a BLM cannon party for a V.Claw(about 1/6 drop), that's about 180 KS needed per claw. At that rate, it's better to farm normal drop mobs and get gil for a claw than to farm KS for a V.Claw and hope for a claw through KS30. This is not meant to discourage you, but to actually help you. If you want to make the most of it then kill EP mobs for both farming and the KS you require. I especially urge you to farm seals if you plan on getting items that are very rare like the Kreigsbeil. Items like those are so rare, only a determined person farming for them will obtain it.