I know protists and animals preceded plants but I am unaware of when fungi arose in relation to plants. At the moment, I cannot find a resource stating how plants evolved from existing kingdoms, or whether they evolved independently from prokaryotes. Thanks for the help, sorry if this is common knowledge.
Plants were almost always considered a separate group from fungi and animals.
As per the latest classification both animals and plants are included in the clade Opisthokonta: animals and related unicellular organisms (holozoa) form a sister clade with holomycota (contains fungi and Cristidiscoidea).
Plants (archaeplastida), aveolates and rhizaria are now grouped under Diaphoretickes (previously they were grouped under Bikonta).
To cut short the plant and animal lineages merge only at the level of the last eukaryotic common ancestor. This means that plants are as unrelated to fungi as they are to animals.
Protista is no longer considered a proper clade. It used to be a group where all unclassified unicellular eukaryotes were dumped. Now these organisms have been reclassified; some are closer to animals (for e.g. Amoeba), some are closer to plants (e.g. Plasmodium) whereas some are part of a group that is distantly related to both plants and animals (for e.g. Euglena).
Have a look at this WikiSpecies site for a detailed classification (latest and historical). It also cites proper references.