This is an extensive list on the location of HM's and TM's in Pokemon Revolution Online
After defeating the 2nd gym leader Misty and finding Bill's book for him, you can go to Vermilion City. South of the city is the boat S.S. Anne, my advice is to talk to every NPC there (it's good training too). After you took the quest to deliver the captain his medicine, you will find Blissey in the ballroom. She will give you the cure for the captain, give the cure to the captain in the captain's cabin, and he will give you the Cut HM.
(You cannot use Fly outside of battle!) Fly is obtainable after completing the Yorkie quest! The Yorkie quest starts at Route 16. Talk to Yorkie, find his brother (his brother is at either power plant, saffron city's poké
(Currently unobtainable/useless outside battle due to the lack of pushable stones)
After defeating the 3rd gym leader Lt. Surge, head out to the Digletts Cave on Route 11. When you arrive at the other side of the cave, head south until you have to walk into a building. There you will find Oak's aide and he will give you the move after you show him 10 caught Pokémon in your Pokédex. :DDDD
TM (from Celadon depth store) Edit
Damage dealing TM's Edit
|TM02||Roar of Time||Normal||Special||100%||80|
Other TM's Edit
|TM04||Whirlwind||Normal||The target is blown away and switched. In the wild, a battle against a single Pokémon will cause the battle to end.||-||-|
|TM45||Thunder wave||Electric||A move that may cause paralysis.||100%|
|TM55||Roar||Normal||The target is scared off and switched. In the wild, a battle against a single Pokémon ends.||-||-|
|TM57||Hail||Ice||Hail creates a hailstorm that lasts for 5 turns||-||-|
|TM61||Sunny Day||Fire||Boosts fire-type moves for 5 turns.||-||-|
|TM62||Taunt||Dark||The target is taunted into a rage that allows it to use only attack moves for three turns.||100%||-|
|TM68||Rain Dance||Water||Boosts water-type moves for 5 turns.||-||-|
|TM87||Sandstorm||Rock||Inflicts damage every turn.||-||-|
|TM114||Rock Smash||Fighting||The user attacks with a punch. This may also lower the target's Defense stat. This move can also shatter rocks in the field.||100%||40|
Talk to the lady at the counter next to the man selling TM's and she will offer to teach your pokemon the move counter. Some TM's like Seismic Toss can also be found while digging.
Other places Edit
TM114 is also given in the building between Route 11 and Route 12 by Oak's Aide if you have captured 30 pokémon. TM19, TM48 can be found with dig. TM07 can be found in Celadon City in Rocket Hideout B3F. TM19 can be found in Route 25. TM09 and TM12 can be found in Mt Moon.