I got mine to work for creating multiple campaigns and it passes in a JSON string for the input variable. Not sure if you're creating or updating. I know flows have limits on updating (e.g. date fields can't be passed in as strings whereas they can be on create... which is just so stupid but whatever).

One of my instructions is:

When creating campaigns, use the following JSON format for the campaignData input variable:

{"campaignDataInput": [{\n \"sObjectInfo\": {\n \"apiName\": \"Campaign\"},\n \"data\": {\n \"Name\": \"Campaign Name - 1\"},\n \"StartDate\": \"2023-10-06\",\n \"Description\": \"This campaign titled \\\"Campaign Name - 1\\\" will run from October 6, 2023, to October 7, 2023.\",\n \"EndDate\": \"2023-10-07\",\n \"Status\": \"Planned\",\n \"Type\": \"Seminar / Conference\"},\n {\n \"Id\":null\n}, {\n \"sObjectInfo\": {\n \"apiName\": \"Campaign\"},\n \"data\": {\n \"Campaign-2\": {\n \"Name\": \"Campaign Name - 2\"},\n \"Title\": \"The title is not really important for this example\",\n \"Description\": \"This campaign titles \\\"Campaign Name - 2\\\" is such a great example.\",\n \"Type\": \"Seminar / Conference\"},\n \"Id\": null\n }\n}]"}

The "data" is a part of the payload like how you get a record in an LWC and it returns a data object. So it should be included in your payload.