Hello Dal, Gregory et al,
Baracca's markings are well documented for at least one of his SPAD VIIs, but his XIII(s) are not so well photographed. I would be inclined to go with the interpretation of his SPAD XIII markings by the three respected Italian author/historian/Illustrators, Roberto Gentilli, Paolo Varriale and Antonio Iozzi in their book on the Italian Aces, published by Schiffer. In this book they illustrate Baracca's SPAD XIII serial S2445 and note that the serial is note known for certain. If the serial IS correct, S2445 was delivered to the 91a squadriglia with four others on 14 February 1918.
The presence of the Cavalino Rampante on the port side of a SPAD XIII flown by Baracca is documented in photographs, but the presence of the Squadriglia's rampant Griffin on the other side is a little open to conjecture. For the SPAD VIIs flown by him, clear photographic evidence exists of the gryphon/griffin being present on the starboard side and the prancing horse on the port. The squadron insignia was introduced during April 1918 and both the SPAD types, VII and XIII were flown by the 91a at the this time, so it is reasonable to suppose that Baracca's XIII carried the horse to port and the Gryphon to starboard.
Regarding the location and presence of roundels, there were certainly none above the wings but the underside is not known for certain. It seems most likely that the red port, starboard green flag colours were worn (note that the centre section was generally left in the standard underside finish and not painted white in MOST cases). The Tail stripes are recorded as (front to back), green white red. It seems possible or even probable that the Bleriot-produced SPAD XIIIs (like S2445) were delivered without national markings applied and these were applied locally - probably at the Aircraft Park. In the case of Baracca's XIII, the red outer ring on the fuselage was painted in the colour order red (outer), white and green (inner) to make it stand out against the camouflaged fuselage.
In conclusion, SPAD XIII 2445 was returned to an aviation park on 21st May and Baracca was killed in a SPAD VII S5382 on 19th June.
All the above is a precis of information contained in the Aces book - it is expensive to buy, but well worth it if you have an interest in the Italian Front airwar. Much of the information is also contained in smaller (and cheaper...) Osprey Italian Aces volume by Paolo Varriale, also highly recommended.