This study found that you get a 90% deactivation of cytomegalovirus when using 40 micrograms of BHT per ml, which works out to an oral dose of around 1.6 grams of BHT, assuming 100% absorption in the gut (since the normal human body contains around 40 liters of fluids).
So a dose of around 1.6 grams of BHT per day is what you would need for a decent antiviral effect.
But regarding the safety of such a dose:
This paper said that the
NOAEL safe intakes for BHT are 25 mg per kg of body weight per day. For a 75 kilo person, that NOAEL limit corresponds to a maximum daily intake of around
1.9 grams of BHT per day. However, the NOAEL limit is defined the
highest dose which still produces no adverse effects — which means that if you go slightly higher than the NOAEL dose, the adverse effects begin. The adverse effects of too high a dose of BHT are the development of hepatocellular carcinomas (liver cancer).
So because the NOAEL safe intake level is the very limit after which things become unsafe, you probably don't really want to be taking any substances at doses near their NOAEL limit, especially when liver cancer is involved.
The acceptable daily intake or
ADI is another measure for safe intake — and a far more cautious one. The ADI safe intake for BHT is set much lower, at just 0.25 mg per kg per day. For a 75 kilo person, that ADI limit corresponds to a maximum daily intake of just around 19 mg of DHT per day — which is safe, but unfortunately not really high enough for antiviral purposes.
However, there does seem to be some contradictory research though: these two studies found BHT had no cancer inducing effects:
Bioassay of butylated hydroxytoluene (BHT) for possible carcinogenicity
Chronic toxicity of butylated hydroxytoluene in Wistar rats
But these two studies found BHT did have cancer inducing effects:
The effects of dietary butylated hydroxytoluene on liver and colon tumor development in mice
A metabolite of butylated hydroxytoluene with potent tumor-promoting activity in mouse lung