The history of the kilt can be a bit of a sticky subject, bound up as it is with romantic ideas of the Highlands and concepts of Scottish nationhood and culture (see the debate surrounding the ideas of Hugh Trevor-Roper for instance). However, in broad terms its historical development is reasonably well understood.
The modern kilt is essentially a product of the early eighteenth century, in so far as that is when it took its current form more or less. It has its antecedent in the belted plaid or feilidh-mór, which developed in the Highlands of Scotland towards the end of the sixteenth century. Essentially this was a large piece of cloth that was gathered up into folds and belted about the waist in order to hold it in place, almost like a Roman toga. It was a versatile multi-purpose garment, well suited to the conditions of the Highlands.
Here is the earliest depiction, an illustration of ‘a Highlander’ from Hieronymus Tielsch, c. 1603-1616 and another example of Scottish mercenaries in Germany from 1631
A modern reconstruction - https://youtu.be/YbAKRffKsPs
The modern kilt is essentially just the bottom half of the feilidh-mór, made easier to wear, stripped of its utilitarian functions and thus transformed into something of cultural rather than practical significance.
Some of the earliest written evidence for the belted plaid actually comes from an Irish source, Lughaidh Ó Cléirigh’s “The Life of Red Hugh O’Donnell” (Beatha Aodha Ruaidh Uí Dhomhnaill). Written in the early 17th century it relates events which took place during the Nine Years War. Describing Scottish mercenaries from the Hebrides, who were employed in O’Donnell’s service in 1594, he states
“These were recognized among the Irish by the difference of their arms and clothing, their habits and language, for their exterior dress was mottled cloaks to the calf of the leg with ties and fastenings. Their girdles were over the loins outside the cloaks.”
That this Irish source notes that there was a difference between the clothing of the Irish and Scottish is interesting because, of course, both were part of a connected Gaelic world, or Gaedhealtacht. Naturally, the clothing worn by Gaels in Scotland was originally more or less the same as that in Ireland, but by this time things had started to diverge (of course fashions and dress do vary from place to place and across, so inevitably we are generalising here).
However, this now brings us more properly to your question. What was the clothing worn by medieval Gaels in Ireland and Scotland? There are two key items of clothing that are mentioned time and again in the sources.
Firstly, there was léine which was a pleated saffron shirt/tunic (or at least dyed to look like saffron). You can see a contemporary 16th century depiction here
However, since you are asking about some sort of cape which might resemble a kilt, the more interesting one - and probably the most significant - is that which would be worn over the léine. This was known to English sources as a ‘mantle’ and in Irish it was called a brat. This was a heavy, thick woolen garment that extended between knee- and ankle-length. Sleeveless and relatively shapeless, it would have been placed over the shoulders and wrapped around the body, and it could be pulled up to cover the head as well. Of course these could vary quite a bit from cheap examples to more ornate ones worn by the Gaelic elite. English writers tended to ignore these differences, and to them the mantle functioned simply as a signifier of cultural and racial difference between themselves and the Irish.
The mantle shared some similarities to the belted plaid in the sense that both could be multi-function garments, suited to the outdoors. Contemporary English sources described the mantle as being able to replace “housing, bedding, and clothing”. Edmund Spenser’s infamous A View to the Present State of Ireland (1596) describes the mantle as “their house, their bed and their garment”. To Spenser, in line with his colonialist views, this was a garment which was “a fit house for an out-law, a meet bed for a rebel, and an apt cloke for a theife”
You can see here one drawing from John Derricke’s The Image of Irelande (1581) which depicts Ruairí Óg Ó Mórdha (Rory Oge O’More) wearing a mantle Here is another famous depiction from Albrecht Dürer
As you can see these mantles were not necessarily any kind of tartan. The poor would wear mantles of loosely woven, coarse and un-dyed wool, while the wealthy would wear finely woven, brightly dyed, woolen mantles with equally bright silk or fine wool fringes. The colours used included greys, browns, blues, and purples. Some Gaelic sources describe “purple mantles” of “bright satin” and d’ainnribh béaltana brat sróil, / . . . / ag cor chorthair iongnáith óir, ie. “of maidens mouth-slender of mantles of satin/ . . . / putting wonderful fringes of gold”.
Another contemporary description by Luke Gernon (1620) states that:
“mantles worn by Irishwomen were “commonly of a browne blew colour with fringe alike, but those that love to be gallant were them of greene, redd, yellow, and other light colours, with fringes diversifyed.”
Naturally English authors didn’t tend to draw attention to the fine craftsmanship of some mantles, but simply lumped them all together as markers of Irishness. Here are a couple more contemporary depictions 1 2
Perhaps some of these mantles would have had some kind of tartan-esque pattern, but it’s not something I have seen mentioned especially. Better evidence for tartan comes - perhaps naturally - from the Scottish parts of the Gaelic world, when the belted plaid was starting to take over from the brat as the more popular fashion as we move from the late 16th and into the 17th century.