Depleted uranium has about 60% of the radioactivity of natural uranium. It therefore can be a risk, with the greatest risk being from inhalation.
A depleted uranium frizzen just sitting there is little risk. The primary radiation given off by depleted uranium is alpha, along with a bit of beta and small amounts of gamma. Alpha particles are blocked by skin, while beta particles are blocked by clothing and by the dead layer of the epidermis. While gamma rays are highly-penetrating, the amount of gamma emitted by depleted uranium is very low. Thus, depleted uranium is not a significant external risk.
It is, however, an internal risk as a chemical and as a radiation emitter. If you ingest DU, about 95% is eliminated in your stool and, of what is taken up in your digestive tract, 2/3 is filtered by your kidneys and into the urine in a short time (1 day).
Inhalation poses a larger risk for retention of the particles of DU.
I would be most concerned about the particles generated when the flint hits the frizzen because that is what would be inhaled. There should be no more than 1 micro-gram per cubic meter of air that you breathe. That tells me that DU is not a terrible risk when inhaled, but not a risk to be taken lightly.
Moral of the story: don't eat your frizzen; don't breathe it in, either.
Ron