The Red Angel Could Be Burnham From the Mirror Universe
The Discovery's journey to the Mirror Universe and back has been referenced surprisingly little in Star Trek: Discovery season 2, with the former emperor Philippa Georgiou serving as the last remaining link to that world. The Discovery was able to travel to the Mirror Universe by way of the spore drive, but there are other ways of travelling between universes (for example, Mirror Lorca switched places with his Prime Universe counterpart due to a transporter malfunction). This leaves open the possibility that others from the Mirror Universe may have secretly traveled to the Prime Universe - Michael Burnham among them.
Admittedly this theory is less likely than the possibility of the Red Angel being a future version of the Prime Universe's Burnham - if only because Star Trek: Discovery season 2 doesn't seem to be gearing up for another Mirror Universe plot (it would be a little repetitive). Moreover, in the tie-in comic Succession, Mirror Burnham was revealed to still be alive when Georgiou was taken to the Prime Universe, but was killed off by the end of the comic - which would seem to nix the possibility of her making an appearance in the show. Co-executive producer Ted Sullivan has said that stories in the comics and novels are "canon unless we do something that invalidates it."
Now that we've looked at the reasons why the Red Angel can't be Mirror Burnham, let's take a look at the possibility that it actually is. If the show decides to ignore Succession and reveal that Mirror Burnham also traveled to the Prime Universe (she was in cahoots with Lorca, so she may have followed him there), she could actually be using the Red Angel guise as a way to lead her Prime Universe counterpart into a trap. This would explain why the Red Angel seems to be so specifically targeting Burnham, and it would be a very interesting twist if the entity that has so far seemed benevolent actually turned out to be season 2's villain. Mirror Burnham could even be leading the Discovery on this chase as part of a scheme cooked up with Mirror Georgiou, whose current goals remain unclear.
There's still the time travel to be explained, of course, but the Red Angel suit could actually be a means of traveling both through time and between different universes. After all, if the technology is unrecognizable to the Federation, it might be because it comes from the Terran Empire.
While both theories about the Red Angel being Michael Burnham could be considered far-fetched, this is a show that recently brought a character back from the dead by revealing that a single tear on his cheek transported his essence into a trans-universal network of space mushrooms, which in turn built him a brand new body, which was then transported back out of the space mushroom network using a gooey cocoon transporter. So... we're not going to write anything off just yet.