Connecting 6 gauge aluminum wiring to 10 gauge copper with AlumiConn
Use a mechanical lug connector ("Polaris" or equivalent)

AlumiConns are only rated for a maximum of 10AWG wire.  For fatter work, you'll want their bigger brothers, mechanical lug connectors (sometimes called "Polaris connectors" after a common brand name) -- the smallest size of them is generally rated for wires anywhere from 14AWG to 4AWG, and as a rule, they are dual-rated for aluminum and copper wire.

You will also likely need a box extension ring or two, as mechanical lug connectors are quite chunky compared to wirenuts or Alumiconns, and you definitely need an appropriate connector to attach the flexible conduit to the box, as right now, it's violating several Code sections by flapping around in the breeze like that.  If the extension rings aren't enough, then you'll have to replace the box with a small (6" by 6" by 4" should be ample) NEMA 1 (indoor) pull box, likely with a flush cover. These are what is used instead of a junction box when splicing large wires, and are available through electrical supply houses.