Hi,
If you are using MapInfo Pro, you can very easily convert the tab files in to GML using the Universal Translator tool. For converting to a KML format we have the Google Earth utility which can export these tab files to KML extension files. To read more about using Universal Translator, have a look at this article: https://li360.pitneybowes.com/s/article/ka180000000Cv8yAAC/MapInfo-Professional-How-to-use-the-Universal-Translator