Make sure you have:

- The Dragon Breastplate itself (obtained from Sir Patrick after having returned the Axe of Stone to the Dwarves).
- The Dragonheart Gem (obtained by finishing the second Warriors' Guild quest).

If you have these two items, Grisha should tell you he'll assemble it for you.

I am in blood
Stepp'd in so far, that, should I wade no more,
Returning were as tedious as go o'er.