We know of no local bird guides on Mayotte.
You can download an excellent trip report sent by Phil Gregory of Sicklebill Safaris in December 2014. All the main islands of the Comoros were visited and all the endemic species were seen. There are details of transport, hotels and other items of value for the visitor.
Planes fly daily between Reunion and Dzaoudzi, the airport / military base in Mayotte. For a return flight from Paris to Mayotte, you would expect to pay at least €800.
Kenya Airways announced flights from Nairobi to Mayotte via Comoros in November 2006. This is an extension of their Paris - Nairobi flights.
The political situation means that Mayotte is difficult to use as a jumping-off point to the other islands. Hopping from island to island can be done by plane. All four islands are connected by a network of shipping routes, and catching boats and ferries is usually the cheapest method of getting from island to island.
October to December are the best months to visit - before the rains set in, but when bird activity is reasonably high. There are adequate hotels and the easiest way to get around Mayotte is with bush taxis ("taxitbrousse") who will take you around the island for a few euros.
See also wikitravel.