Some OTC products already contain vitC and zinc in proper amounts, e.g. Sambucol (not affiliated).
[1] https://en.m.wikipedia.org/wiki/Zinc_and_the_common_cold
I would not take zinc in the same numbers as Vitamin C - but exactly therefor eI said I would take them apart, because, at least in the German and Spanish Market, you have combination preparates with 80mg Vitramin C and 5mg of Zinc - to achieve the effects I observed in myself you'd need 3x10 of these for the Vitamin C amount, whioch would be a lot of zinc which I would not recommend and have no experience with and no knowledge about the risks.
The articles seem to not agree in doses and helpfulness - one says it must be >= 75mg to actually do something, another that even 90+ mg doesn't do anything. And I believe to remember that already from 25mg/day you can get strange effects in the belly as side effects...
The thing is as with Vitamin C, most supermarket products just have low doses. So to get an effect i recommend getting pure and high dosed preparates of both, each by itself.