The Setup
I run a game using milestone XP, but rather than coming up with plot points, I planned out how many sessions we'll go between each level. This is because I felt like I was being internally inconsistent with when players leveled up, but I hate tracking XP.
I came to these numbers by looking at the general trends of how much XP it takes to get between various levels by default, and by adjusting based on how long I wanted to spend running this campaign. The XP chart doesn't follow a smooth function, but instead takes some weird dips, which I assumed were on purpose, and tried to incorporate into my chart. This means that I have a leveling chart, just not with tracking XP.
The Table
This is the table I've been using, but obviously, this is just what works for me. It might not fit other people's games, and that's fine. It's mostly here as an example.
Level |
Sessions to next level |
\$\qquad\qquad\$ |
Level |
Sessions to next level |
1 |
2 |
|
11 |
8 |
2 |
2 |
|
12 |
6 |
3 |
3 |
|
13 |
6 |
4 |
4 |
|
14 |
7 |
5 |
4 |
|
15 |
7 |
6 |
6 |
|
16 |
7 |
7 |
6 |
|
17 |
8 |
8 |
7 |
|
18 |
8 |
9 |
7 |
|
19 |
6 |
10 |
6 |
|
|
|
The Solution
Using this, I would look at how many levels the XP from the item, be it the Deck of Many Things or something else, would grant in an XP leveling system.
To continue with your example, the Fool takes 1/3 of a level from a level 15 character. In my table, going from level 15 to level 16 takes 7 sessions, so I would make a note that that unlucky person will need 2 extra sessions to reach level 16. Or, if they draw the Jester, they'll level up 2 sessions early.
I keep track of this next to my notes on each session, which are separated and dated for each game; this makes it easy for me to keep track of when people should be leveling up.
The reason I go into all this detail is that I'm not sure, without some sort of standardized alternative to the XP charts, how to implement this, other than sort of winging it, which would feel unsatisfactory to me both as a DM and as a player.