Currently, the Blades are Esbern, Delphine, Dragonborn and 3 recruits. Delphine have an inn in Riverwood, but i don't think it is enough to support them in the long run in their crusade against dragons and maybe in the future fighting the Thalmor. The Dragonborn maybe rich though, but he/she alone surely cannot rise an immediate army, there are a lot of mouth to feed

The Companions are mercenary, they got paid for their job...Greybeards have the villagers who dare the monsters along the path and climb 7000 steps to sent their food.....but The Blades now do their job for free.

Before, the government who pay them, now, they are alone, and i am surprise how the new recruits are "willingly" join them for free (I blame Bethesda for that).

So, how the Dragonborn want to lead The Blades, rebuild the order and make it a functional organization?

I don't want them to become a gang of mercenary in the future, i want them to be a respectable, mysterious and well established organization.

I suspect that they will probably fund themselves much the way the KotN would have. The gear is already there. As far as an army? I don't think that's how the blades would function. It's more of a cause than a group. Just my personal opinion.