Well, here is a MSDS for black powder (PDF); it doesn’t say much on the hazards of ingestion other than to induce vomiting if swallowed. As for the ingredients, the main ingredients are either sodium or potassium nitrate; which can cause sodium or potassium poisoning respectively, although the LD50s for these from their respective MSDSs are on the order of 1-2 grams per kg, so a 70 kg human would have to ingest around 70-140 grams for a fatal dose (less just to get sick, say maybe 10% of that as an upper limit, 7-14 grams or around 10-20 grams* of black powder, which is around 70% nitrate). The other ingredients are charcoal and sulfur, possibly a trace of graphite, which are relatively non-toxic, (in the relative amounts, the MSDS for sulfur says that small amounts won’t cause health effects; they are also relatively insoluble, unlike the nitrates, and make up only 3-6 grams of the 10-20 grams calculated from the nitrates alone).
*Just an assumption based on the LD50 and what amount might start to make you sick. Also, as a check, assuming that only the Na/K is toxic, you can compare it to table salt; e.g. NaNO3 is 27% while NaCl is 40% sodium by weight and people regularly consume 5-6 grams of salt (some even more, up to 2x this much) a day, equivalent to the amount of sodium in 7.4-8.9 grams of NaNO3, which falls within the range I estimated as a non-toxic dose (mind that ingesting it all at once isn’t the same as over 24 hours).