You can play Story, Kotfe/Kotet, and [SOLO] Flashpoints and Expansion Stories as a Group or Co-Op with Friends in SWTOR.

Despite some content being labeled [SOLO] or [SOLO-Story], SWTOR allows you to still group up with other players if you are having a tough time, you simply cannot progress both players Story Quests at once.
This means if you are both on the same KOTFE/ET chapter or Flashpoint such as Objective Meridian you must do it twice, once for each player.

It is very easy to invite any other player in your Group to a [STORY] or [SOLO] Quest or Flashpoint, once the other players are in your Group, right click your characters portrait (Face next to health bar), and click the Group Option, then the ‘Summon Group for Story Quest’ button. All other players in your Group will be sent a free Teleport to your exact location in the Story and will be able to help you out in Combat and Adventuring while you still have full control of the Cutscenes.

This works for:
All KOTFE chapters and difficulties.
All KOTET chapters and difficulties.
Iokath planet Storyline.
Fractured Alliances Flashpoint Storyline (Umbara, Copero, Nathema).
Jedi Under Siege (Ossus).
Onslaught (Onderon, Mek-Sha, Objective Meridian).
Echoes of Oblivion (Tenebrae, Spirit of Vengeance).
Secrets of the Enclave (Dantooine Flashpoint).
Legacy of the Sith (Manaan, Elom Flashpoint).
Ruhnuk Storyline.

The only [SOLO] content that you are NOT allowed to summon other players in, is the Eternal Championship minigame on Zakuul, if you wish to invite others you must pick the [SOLO+] option before starting.