if the hose gets kink while the pump is running will it burn the pump out?
Yes. A brief stoppage as Fitter30 mentioned, will not be a problem, but pumps typically require at least 1 GPM flow to keep the motor cool.
Deep well pumps are most often equipped with a pressure tank and pressure switch. With those devices, there will be no need to always manually shut off power to the pump as stopping water flow will cause the pump to continue running to fill the pressure tank until the system pressure has risen to the pressure switch cut-out pressure which will shut off the pump. When a faucet or garden hose is opened, water will initially flow from the pressure tank until the system pressure drops to the pressure switch cut-in pressure whereby the pump will become activated.
Unless 100% of the pump's GPM capacity is always flowing from the faucet or hose, any excess capacity will slowly refill the pressure tank and so the pump will cycle Off & On continually every few minutes. To prevent the pump from cycling and to achieve consistant pressure regardless of the GPM flow rate, consider equipping your system with a Cycle Stop valve such as included in the PK1A kit which not only includes a CSV, but also a pressure tank and pressure switch. See link below.
PK1A kit