I can’t find anything on timing. Since the zinc-ionophore acts as an emulsifier (allowing zinc through the fatty cell wall) it would make sense to me to take it a with the zinc.
https://www.sciencedirect.com/science/article/pii/S2210803320300531
Useful dosage and cautions information in the conclusion (pasted blelow):
9. Conclusion
Having a range of bioactive components such as thymoquinone and nigellimine, black seed might offer a number of benefits to treat COVID-19 such as (i) blocking the entry of the virus into pneumocytes and (ii) providing ionophore for enhanced uptake of Zn2+ which in turn can enhance host immune response against SARS-CoV-2 as well as inhibit its replication by blocking the viral RdRp. However, it is important to identify the right doses for both black seed or its derivatives such as oil, as well as for Zn. It can be noted that black seed oil has been used at doses of between 40−80 mg/kg/day as adjunctive therapy without any side effects. On the other hand, Zn intake above its recommended daily allowance (RDA) might be harmful which varies according to age, sex and other health conditions. For example, the RDA varies for children 1–8 years old (3−5 mg), males 9–13 years (8 mg), males > 14 years (11 mg), females > 18 years (8 mg), and females 14–18 years (9 mg). Individuals with health conditions such as with liver and kidney diseases as well as pregnant women must consult the physicians before deciding to take any self-prescribed Zn supplement.
Zinc and Quercetin: Importance During Pandemic, December 27, 2021