There is no API to fetch this information as the marketing system is really generic and have loads of possibilities. What you can do is properly to fetch the specific campaign using the CampaignService and then loop the rules and find your rule and the currency settings for it and use that to print on the webshop.

After alot of noodeling i figured this out. I'll post the code here for anyone else wanting to do this:

    public decimal getCurrentFreeShippingLimit() {

        // Get the campaign by name
        IEnumerable<Campaign> campaigns = CampaignService.Instance.GetAllActive(storeId).Where(campaign => (campaign.Name == "Gratis fragt"));
        Campaign freeShipping = campaigns.First();

        // Get the first rule of the first group
        OrderAmountRule rule = (OrderAmountRule)freeShipping.RulesGroups.First().Rules.First();

        // Get the rule that corresponds to the current currency
        Currency currency = TC.GetCurrentCurrency(storeId);
        KeyValuePair<long, decimal> shippingAmonut = rule.Amounts.Where(amount => amount.Key == currency.Id).First();

        // Output the value, ie. the free shipping cutoff point
        return shippingAmonut.Value;

    }

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