TXCn в отсутствие прерывания надо СБРАСЫВАТЬ РУЧКАМИ.
Для UDREn этого не надо, т.к. он сбрасывается фактом записи в UDRn

PS Цитирую:
• Bit 6 – TXCn: USART Transmit Complete
This flag bit is set when the entire frame in the Transmit Shift Register has been shifted
out and there are no new data currently present in the transmit buffer (UDRn). The
TXCn flag bit is automatically cleared when a transmit complete interrupt is executed, or
it can be cleared by writing a one to its bit location. The TXCn flag can generate a Transmit
Complete interrupt (see description of the TXCIEn bit).
• Bit 5 – UDREn: USART Data Register Empty
The UDREn flag indicates if the transmit buffer (UDRn) is ready to receive new data. If
UDREn is one, the buffer is empty, and therefore ready to be written. The UDREn flag
can generate a Data Register Empty interrupt (see description of the UDRIEn bit).
UDREn is set after a reset to indicate that the Transmitter is ready.